Question 1
Evaluate
a) $\sqrt9$
a
$3$
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b) $\sqrt{25}$
a
$5$
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c) $\sqrt{49}$
a
$7$
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d) $\sqrt{121}$
a
$11$
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e) $\sqrt{4}$
a
$2$
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f) $\sqrt{64}$
a
$8$
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g) $\sqrt{144}$
a
$12$
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h) $\sqrt{1}$
a
$10$
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Question 2
Type the following into a calculator and round to $2$ decimal places.
a) $\sqrt3$
a
$1.73$
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b) $\sqrt5$
a
$2.224$
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c) $\sqrt{10}$
a
$3.16$
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d) $\sqrt{19}$
a
$4.36$
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e) $\sqrt{20}$
a
$4.47$
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f) $\sqrt{2}$
a
$1.41$
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g) $\sqrt{11}$
a
$3.32$
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h) $\sqrt{26}$
a
$5.10$
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Question 3
Simplify
a) $\left(\sqrt9\right)^2$
a
$9$
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b) $\left(\sqrt{25}\right)^2$
a
$25$
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c) $\left(\sqrt{5}\right)^2$
a
$5$
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d) $\left(\sqrt{2}\right)^2$
a
$2$
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e) $\left(\sqrt{19}\right)^2$
a
$19$
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f) $\left(\sqrt{100}\right)^2$
a
$100$
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g) $\left(\sqrt{115}\right)^2$
a
$115$
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h) $\left(\sqrt{738}\right)^2$
a
$738$
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Question 4
Classify the following as rational or irrational numbers
a) $5$
a
Rational
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b) $\frac12$
a
Rational
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c) $0.7$
a
Rational
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d) $0.\dot3$
a
Rational. This number follows a pattern and can be written as a fraction ($\frac13$)
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e) $0.9384759287583...$
a
Irrational. This number follows no pattern and continues with no pattern and cannot be written as a fraction.
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f) $\sqrt3$
a
Irrational $\sqrt3=1.73205080757...$ which continues with no pattern and cannot be written as a fraction.
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g) $0.\dot1\dot3$
a
Rational. This number follows a pattern and can be written as a fraction ($\frac{13}{99}$)
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h) $\sqrt{18}$
a
Irrational $\sqrt{18}=4.242640687...$ which continues with no pattern and cannot be written as a fraction.
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Question 5
Classify the following as surds or a rational number
a) $\sqrt3$
a
Surd
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b) $\sqrt7$
a
Surd
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c) $3$
a
Rational number
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d) $\sqrt9$
a
Rational number as $\sqrt9=3$ which is not an irrational number.
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e) $\sqrt{\frac{4}{9}}$
a
Rational number as $\sqrt{{\frac{4}{9}}=\frac23$ which is not an irrational number.
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f) $\sqrt{\frac{5}{9}}$
a
Surd
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g) $\sqrt{0.1}$
a
Surd
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h) $\sqrt{0.16}$
a
Rational number as $\sqrt{0.16}=\sqrt{{4}{25}}=\frac25$ which is not an irrational number.
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Question 6
Simplify
a) $\left(\sqrt3\right)^4$
a
$9$
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$\left(\sqrt3\right)^4=\left(\left(\sqrt3\right)^2\right)^2=3^2=9$
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b) $\left(\sqrt5\right)^4$
a
$25$
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c) $\left(\sqrt{9}\right)^4$
a
$81$
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d) $\left(\sqrt{2}\right)^6$
a
$8$
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e) $\left(\sqrt{3}\right)^6$
a
$27$
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f) $\left(\sqrt{2}\right)^8$
a
$16$
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g) $\left(\sqrt{16}\right)^3$
a
$64$
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h) $\left(\sqrt{25}\right)^3$
a
$125$
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Question 7
Evaluate
a) $2\times\sqrt3$
a
$2\sqrt3$
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b) $3\times\sqrt7$
a
$3\sqrt7$
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c) $4\times2\sqrt5$
a
$8\sqrt5$
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d) $8\times3\sqrt{10}$
a
$24\sqrt{10}$
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e) $5\times5\sqrt{21}$
a
$25\sqrt{21}$
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f) $3\times\sqrt{25}$
a
$15$
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g) $2\sqrt{36}$
a
$12$
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h) $8\times3\sqrt{64}$
a
$192$
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Question 8
Evaluate
a) $\sqrt2\times\sqrt2$
a
$2$
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b) $\sqrt7\times\sqrt7$
a
$7$
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c) $\sqrt9\times\sqrt9$
a
$9$
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d) $\sqrt{42}\times\sqrt{42}$
a
$42$
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e) $\sqrt{5}\times\sqrt5\times\sqrt5$
a
$5\sqrt5$
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f) $\sqrt2\times\sqrt2\times\sqrt2$
a
$2\sqrt2$
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g) $\sqrt{16}\times\sqrt{16}\times\sqrt{16}$
a
$64$
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h) $3\times\sqrt{11}\times\sqrt{11}\times\sqrt{11}$
a
$33\sqrt{11}$
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Question 9
Simplify
a) $\sqrt3+\sqrt3$
a
$2\sqrt3$
Question ID: 10330090010
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b) $\sqrt6+\sqrt6$
a
$2\sqrt6$
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c) $\sqrt5+\sqrt5+\sqrt5$
a
$3\sqrt5$
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d) $\sqrt{11}+\sqrt{11}+\sqrt{11}+\sqrt{11}$
a
$4\sqrt{11}$
Question ID: 10330090040
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e) $2\sqrt{13}+\sqrt{13}$
a
$3\sqrt{13}$
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f) $3\sqrt{22}+2\sqrt{22}$
a
$5\sqrt{22}$
Question ID: 10330090060
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g) $5\sqrt{7}+3\times\sqrt{7}$
a
$8\sqrt7$
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h) $13\times\sqrt{39}+2\times\sqrt{39}+\sqrt{39}$
a
$16\sqrt{39}$
Question ID: 10330090080
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Question 10
Simplify
a) $2\sqrt3-\sqrt3$
a
$\sqrt3$
Question ID: 10330100010
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b) $5\sqrt{15}-\sqrt{15}$
a
$4\sqrt{15}$
Question ID: 10330100020
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c) $10\sqrt{21}-2\sqrt{21}$
a
$8\sqrt{21}$
Question ID: 10330100030
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d) $15\sqrt{15}-5\times\sqrt{15}$
a
$10\sqrt{15}$
Question ID: 10330100040
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e) $11\times\sqrt{43}-11\sqrt{43}$
a
$0$
Question ID: 10330100050
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f) $92\times\sqrt{94}-100\sqrt{94}$
a
$-8\sqrt{94}$
Question ID: 10330100060
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g) $22\sqrt4-10\times\sqrt4$
a
$24$
Question ID: 10330100070
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h) $\sqrt{14}-2\sqrt{14}-33\times\sqrt{14}$
a
$-34\sqrt{14}$
Question ID: 10330100080
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Question 11
Simplify
a) $\sqrt3\times\sqrt3+\sqrt5$
a
$3+\sqrt5$
Question ID: 10330110010
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b) $\left(\sqrt{19}\right)^2+\sqrt{19}$
a
$19+\sqrt{19}$
Question ID: 10330110020
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c) $\left(\sqrt{7}\right)^2+\left(\sqrt{7}\right)^4$
a
$56$
Question ID: 10330110030
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d) $\left(\sqrt{3}\right)^3$
a
$3\sqrt3$
Question ID: 10330110040
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e) $\left(\sqrt{11}\right)^3$
a
$11\sqrt{11}$
Question ID: 10330110050
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f) $\left(\sqrt{2}\right)^5$
a
$4\sqrt2$
Question ID: 10330110060
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g) $\sqrt6\times5\times\sqrt6\times3$
a
$90$
Question ID: 10330110070
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h) $\left(\sqrt{10}\right)^2\times5\times\sqrt{10}\times\sqrt9$
a
$150\sqrt{10}$
Question ID: 10330110080
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Question 1
Evaluate
a) $\sqrt9$
b) $\sqrt{25}$
c) $\sqrt{49}$
d) $\sqrt{121}$
e) $\sqrt{4}$
f) $\sqrt{64}$
g) $\sqrt{144}$
h) $\sqrt{1}$
Question 2
Type the following into a calculator and round to $2$ decimal places.
a) $\sqrt3$
b) $\sqrt5$
c) $\sqrt{10}$
d) $\sqrt{19}$
e) $\sqrt{20}$
f) $\sqrt{2}$
g) $\sqrt{11}$
h) $\sqrt{26}$
Question 3
Simplify
a) $\left(\sqrt9\right)^2$
b) $\left(\sqrt{25}\right)^2$
c) $\left(\sqrt{5}\right)^2$
d) $\left(\sqrt{2}\right)^2$
e) $\left(\sqrt{19}\right)^2$
f) $\left(\sqrt{100}\right)^2$
g) $\left(\sqrt{115}\right)^2$
h) $\left(\sqrt{738}\right)^2$
Question 4
Classify the following as rational or irrational numbers
a) $5$
b) $\frac12$
c) $0.7$
d) $0.\dot3$
e) $0.9384759287583...$
f) $\sqrt3$
g) $0.\dot1\dot3$
h) $\sqrt{18}$
Question 5
Classify the following as surds or a rational number
a) $\sqrt3$
b) $\sqrt7$
c) $3$
d) $\sqrt9$
e) $\sqrt{\frac{4}{9}}$
f) $\sqrt{\frac{5}{9}}$
g) $\sqrt{0.1}$
h) $\sqrt{0.16}$
Question 6
Simplify
a) $\left(\sqrt3\right)^4$
b) $\left(\sqrt5\right)^4$
c) $\left(\sqrt{9}\right)^4$
d) $\left(\sqrt{2}\right)^6$
e) $\left(\sqrt{3}\right)^6$
f) $\left(\sqrt{2}\right)^8$
g) $\left(\sqrt{16}\right)^3$
h) $\left(\sqrt{25}\right)^3$
Question 7
Evaluate
a) $2\times\sqrt3$
b) $3\times\sqrt7$
c) $4\times2\sqrt5$
d) $8\times3\sqrt{10}$
e) $5\times5\sqrt{21}$
f) $3\times\sqrt{25}$
g) $2\sqrt{36}$
h) $8\times3\sqrt{64}$
Question 8
Evaluate
a) $\sqrt2\times\sqrt2$
b) $\sqrt7\times\sqrt7$
c) $\sqrt9\times\sqrt9$
d) $\sqrt{42}\times\sqrt{42}$
e) $\sqrt{5}\times\sqrt5\times\sqrt5$
f) $\sqrt2\times\sqrt2\times\sqrt2$
g) $\sqrt{16}\times\sqrt{16}\times\sqrt{16}$
h) $3\times\sqrt{11}\times\sqrt{11}\times\sqrt{11}$
Question 9
Simplify
a) $\sqrt3+\sqrt3$
b) $\sqrt6+\sqrt6$
c) $\sqrt5+\sqrt5+\sqrt5$
d) $\sqrt{11}+\sqrt{11}+\sqrt{11}+\sqrt{11}$
e) $2\sqrt{13}+\sqrt{13}$
f) $3\sqrt{22}+2\sqrt{22}$
g) $5\sqrt{7}+3\times\sqrt{7}$
h) $13\times\sqrt{39}+2\times\sqrt{39}+\sqrt{39}$
Question 10
Simplify
a) $2\sqrt3-\sqrt3$
b) $5\sqrt{15}-\sqrt{15}$
c) $10\sqrt{21}-2\sqrt{21}$
d) $15\sqrt{15}-5\times\sqrt{15}$
e) $11\times\sqrt{43}-11\sqrt{43}$
f) $92\times\sqrt{94}-100\sqrt{94}$
g) $22\sqrt4-10\times\sqrt4$
h) $\sqrt{14}-2\sqrt{14}-33\times\sqrt{14}$
Question 11
Simplify
a) $\sqrt3\times\sqrt3+\sqrt5$
b) $\left(\sqrt{19}\right)^2+\sqrt{19}$
c) $\left(\sqrt{7}\right)^2+\left(\sqrt{7}\right)^4$
d) $\left(\sqrt{3}\right)^3$
e) $\left(\sqrt{11}\right)^3$
f) $\left(\sqrt{2}\right)^5$
g) $\sqrt6\times5\times\sqrt6\times3$
h) $\left(\sqrt{10}\right)^2\times5\times\sqrt{10}\times\sqrt9$
Answers
Question 1
a) $3$
b) $5$
c) $7$
d) $11$
e) $2$
f) $8$
g) $12$
h) $10$
Question 2
a) $1.73$
b) $2.224$
c) $3.16$
d) $4.36$
e) $4.47$
f) $1.41$
g) $3.32$
h) $5.10$
Question 3
a) $9$
b) $25$
c) $5$
d) $2$
e) $19$
f) $100$
g) $115$
h) $738$
Question 4
a) Rational
b) Rational
c) Rational
d) Rational. This number follows a pattern and can be written as a fraction ($\frac13$)
e) Irrational. This number follows no pattern and continues with no pattern and cannot be written as a fraction.
f) Irrational $\sqrt3=1.73205080757...$ which continues with no pattern and cannot be written as a fraction.
g) Rational. This number follows a pattern and can be written as a fraction ($\frac{13}{99}$)
h) Irrational $\sqrt{18}=4.242640687...$ which continues with no pattern and cannot be written as a fraction.
Question 5
a) Surd
b) Surd
c) Rational number
d) Rational number as $\sqrt9=3$ which is not an irrational number.
e) Rational number as $\sqrt{{\frac{4}{9}}=\frac23$ which is not an irrational number.
f) Surd
g) Surd
h) Rational number as $\sqrt{0.16}=\sqrt{{4}{25}}=\frac25$ which is not an irrational number.
Question 6
a) $9$
b) $25$
c) $81$
d) $8$
e) $27$
f) $16$
g) $64$
h) $125$
Question 7
a) $2\sqrt3$
b) $3\sqrt7$
c) $8\sqrt5$
d) $24\sqrt{10}$
e) $25\sqrt{21}$
f) $15$
g) $12$
h) $192$
Question 8
a) $2$
b) $7$
c) $9$
d) $42$
e) $5\sqrt5$
f) $2\sqrt2$
g) $64$
h) $33\sqrt{11}$
Question 9
a) $2\sqrt3$
b) $2\sqrt6$
c) $3\sqrt5$
d) $4\sqrt{11}$
e) $3\sqrt{13}$
f) $5\sqrt{22}$
g) $8\sqrt7$
h) $16\sqrt{39}$
Question 10
a) $\sqrt3$
b) $4\sqrt{15}$
c) $8\sqrt{21}$
d) $10\sqrt{15}$
e) $0$
f) $-8\sqrt{94}$
g) $24$
h) $-34\sqrt{14}$
Question 11
a) $3+\sqrt5$
b) $19+\sqrt{19}$
c) $56$
d) $3\sqrt3$
e) $11\sqrt{11}$
f) $4\sqrt2$
g) $90$
h) $150\sqrt{10}$
Question 1
Evaluate
a) $\sqrt9$
b) $\sqrt{25}$
c) $\sqrt{49}$
d) $\sqrt{121}$
e) $\sqrt{4}$
f) $\sqrt{64}$
g) $\sqrt{144}$
h) $\sqrt{1}$
Question 2
Type the following into a calculator and round to $2$ decimal places.
a) $\sqrt3$
b) $\sqrt5$
c) $\sqrt{10}$
d) $\sqrt{19}$
e) $\sqrt{20}$
f) $\sqrt{2}$
g) $\sqrt{11}$
h) $\sqrt{26}$
Question 3
Simplify
a) $\left(\sqrt9\right)^2$
b) $\left(\sqrt{25}\right)^2$
c) $\left(\sqrt{5}\right)^2$
d) $\left(\sqrt{2}\right)^2$
e) $\left(\sqrt{19}\right)^2$
f) $\left(\sqrt{100}\right)^2$
g) $\left(\sqrt{115}\right)^2$
h) $\left(\sqrt{738}\right)^2$
Question 4
Classify the following as rational or irrational numbers
a) $5$
b) $\frac12$
c) $0.7$
d) $0.\dot3$
e) $0.9384759287583...$
f) $\sqrt3$
g) $0.\dot1\dot3$
h) $\sqrt{18}$
Question 5
Classify the following as surds or a rational number
a) $\sqrt3$
b) $\sqrt7$
c) $3$
d) $\sqrt9$
e) $\sqrt{\frac{4}{9}}$
f) $\sqrt{\frac{5}{9}}$
g) $\sqrt{0.1}$
h) $\sqrt{0.16}$
Question 6
Simplify
a) $\left(\sqrt3\right)^4$
b) $\left(\sqrt5\right)^4$
c) $\left(\sqrt{9}\right)^4$
d) $\left(\sqrt{2}\right)^6$
e) $\left(\sqrt{3}\right)^6$
f) $\left(\sqrt{2}\right)^8$
g) $\left(\sqrt{16}\right)^3$
h) $\left(\sqrt{25}\right)^3$
Question 7
Evaluate
a) $2\times\sqrt3$
b) $3\times\sqrt7$
c) $4\times2\sqrt5$
d) $8\times3\sqrt{10}$
e) $5\times5\sqrt{21}$
f) $3\times\sqrt{25}$
g) $2\sqrt{36}$
h) $8\times3\sqrt{64}$
Question 8
Evaluate
a) $\sqrt2\times\sqrt2$
b) $\sqrt7\times\sqrt7$
c) $\sqrt9\times\sqrt9$
d) $\sqrt{42}\times\sqrt{42}$
e) $\sqrt{5}\times\sqrt5\times\sqrt5$
f) $\sqrt2\times\sqrt2\times\sqrt2$
g) $\sqrt{16}\times\sqrt{16}\times\sqrt{16}$
h) $3\times\sqrt{11}\times\sqrt{11}\times\sqrt{11}$
Question 9
Simplify
a) $\sqrt3+\sqrt3$
b) $\sqrt6+\sqrt6$
c) $\sqrt5+\sqrt5+\sqrt5$
d) $\sqrt{11}+\sqrt{11}+\sqrt{11}+\sqrt{11}$
e) $2\sqrt{13}+\sqrt{13}$
f) $3\sqrt{22}+2\sqrt{22}$
g) $5\sqrt{7}+3\times\sqrt{7}$
h) $13\times\sqrt{39}+2\times\sqrt{39}+\sqrt{39}$
Question 10
Simplify
a) $2\sqrt3-\sqrt3$
b) $5\sqrt{15}-\sqrt{15}$
c) $10\sqrt{21}-2\sqrt{21}$
d) $15\sqrt{15}-5\times\sqrt{15}$
e) $11\times\sqrt{43}-11\sqrt{43}$
f) $92\times\sqrt{94}-100\sqrt{94}$
g) $22\sqrt4-10\times\sqrt4$
h) $\sqrt{14}-2\sqrt{14}-33\times\sqrt{14}$
Question 11
Simplify
a) $\sqrt3\times\sqrt3+\sqrt5$
b) $\left(\sqrt{19}\right)^2+\sqrt{19}$
c) $\left(\sqrt{7}\right)^2+\left(\sqrt{7}\right)^4$
d) $\left(\sqrt{3}\right)^3$
e) $\left(\sqrt{11}\right)^3$
f) $\left(\sqrt{2}\right)^5$
g) $\sqrt6\times5\times\sqrt6\times3$
h) $\left(\sqrt{10}\right)^2\times5\times\sqrt{10}\times\sqrt9$
Answers
Question 1
a) $3$
b) $5$
c) $7$
d) $11$
e) $2$
f) $8$
g) $12$
h) $10$
Question 2
a) $1.73$
b) $2.224$
c) $3.16$
d) $4.36$
e) $4.47$
f) $1.41$
g) $3.32$
h) $5.10$
Question 3
a) $9$
b) $25$
c) $5$
d) $2$
e) $19$
f) $100$
g) $115$
h) $738$
Question 4
a) Rational
b) Rational
c) Rational
d) Rational. This number follows a pattern and can be written as a fraction ($\frac13$)
e) Irrational. This number follows no pattern and continues with no pattern and cannot be written as a fraction.
f) Irrational $\sqrt3=1.73205080757...$ which continues with no pattern and cannot be written as a fraction.
g) Rational. This number follows a pattern and can be written as a fraction ($\frac{13}{99}$)
h) Irrational $\sqrt{18}=4.242640687...$ which continues with no pattern and cannot be written as a fraction.
Question 5
a) Surd
b) Surd
c) Rational number
d) Rational number as $\sqrt9=3$ which is not an irrational number.
e) Rational number as $\sqrt{{\frac{4}{9}}=\frac23$ which is not an irrational number.
f) Surd
g) Surd
h) Rational number as $\sqrt{0.16}=\sqrt{{4}{25}}=\frac25$ which is not an irrational number.
Question 6
a) $9$
b) $25$
c) $81$
d) $8$
e) $27$
f) $16$
g) $64$
h) $125$
Question 7
a) $2\sqrt3$
b) $3\sqrt7$
c) $8\sqrt5$
d) $24\sqrt{10}$
e) $25\sqrt{21}$
f) $15$
g) $12$
h) $192$
Question 8
a) $2$
b) $7$
c) $9$
d) $42$
e) $5\sqrt5$
f) $2\sqrt2$
g) $64$
h) $33\sqrt{11}$
Question 9
a) $2\sqrt3$
b) $2\sqrt6$
c) $3\sqrt5$
d) $4\sqrt{11}$
e) $3\sqrt{13}$
f) $5\sqrt{22}$
g) $8\sqrt7$
h) $16\sqrt{39}$
Question 10
a) $\sqrt3$
b) $4\sqrt{15}$
c) $8\sqrt{21}$
d) $10\sqrt{15}$
e) $0$
f) $-8\sqrt{94}$
g) $24$
h) $-34\sqrt{14}$
Question 11
a) $3+\sqrt5$
b) $19+\sqrt{19}$
c) $56$
d) $3\sqrt3$
e) $11\sqrt{11}$
f) $4\sqrt2$
g) $90$
h) $150\sqrt{10}$