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Number - Surds

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Question 1


Evaluate

a) $\sqrt9$  a s v
b) $\sqrt{25}$  a s v
c) $\sqrt{49}$  a s v
d) $\sqrt{121}$  a s v
e) $\sqrt{4}$  a s v
f) $\sqrt{64}$  a s v
g) $\sqrt{144}$  a s v
h) $\sqrt{1}$  a s v


Question 2


Type the following into a calculator and round to $2$ decimal places.

a) $\sqrt3$  a s v
b) $\sqrt5$  a s v
c) $\sqrt{10}$  a s v
d) $\sqrt{19}$  a s v
e) $\sqrt{20}$  a s v
f) $\sqrt{2}$  a s v
g) $\sqrt{11}$  a s v
h) $\sqrt{26}$  a s v


Question 3


Simplify

a) $\left(\sqrt9\right)^2$  a s v
b) $\left(\sqrt{25}\right)^2$  a s v
c) $\left(\sqrt{5}\right)^2$  a s v
d) $\left(\sqrt{2}\right)^2$  a s v
e) $\left(\sqrt{19}\right)^2$  a s v
f) $\left(\sqrt{100}\right)^2$  a s v
g) $\left(\sqrt{115}\right)^2$  a s v
h) $\left(\sqrt{738}\right)^2$  a s v


Question 4


Classify the following as rational or irrational numbers

a) $5$  a s v
b) $\frac12$  a s v
c) $0.7$  a s v
d) $0.\dot3$  a s v
e) $0.9384759287583...$  a s v
f) $\sqrt3$  a s v
g) $0.\dot1\dot3$  a s v
h) $\sqrt{18}$  a s v


Question 5


Classify the following as surds or a rational number

a) $\sqrt3$  a s v
b) $\sqrt7$  a s v
c) $3$  a s v
d) $\sqrt9$  a s v
e) $\sqrt{\frac{4}{9}}$  a s v
f) $\sqrt{\frac{5}{9}}$  a s v
g) $\sqrt{0.1}$  a s v
h) $\sqrt{0.16}$  a s v


Question 6


Simplify

a) $\left(\sqrt3\right)^4$  a s v
b) $\left(\sqrt5\right)^4$  a s v
c) $\left(\sqrt{9}\right)^4$  a s v
d) $\left(\sqrt{2}\right)^6$  a s v
e) $\left(\sqrt{3}\right)^6$  a s v
f) $\left(\sqrt{2}\right)^8$  a s v
g) $\left(\sqrt{16}\right)^3$  a s v
h) $\left(\sqrt{25}\right)^3$  a s v


Question 7


Evaluate

a) $2\times\sqrt3$  a s v
b) $3\times\sqrt7$  a s v
c) $4\times2\sqrt5$  a s v
d) $8\times3\sqrt{10}$  a s v
e) $5\times5\sqrt{21}$  a s v
f) $3\times\sqrt{25}$  a s v
g) $2\sqrt{36}$  a s v
h) $8\times3\sqrt{64}$  a s v


Question 8


Evaluate

a) $\sqrt2\times\sqrt2$  a s v
b) $\sqrt7\times\sqrt7$  a s v
c) $\sqrt9\times\sqrt9$  a s v
d) $\sqrt{42}\times\sqrt{42}$  a s v
e) $\sqrt{5}\times\sqrt5\times\sqrt5$  a s v
f) $\sqrt2\times\sqrt2\times\sqrt2$  a s v
g) $\sqrt{16}\times\sqrt{16}\times\sqrt{16}$  a s v
h) $3\times\sqrt{11}\times\sqrt{11}\times\sqrt{11}$  a s v


Question 9


Simplify

a) $\sqrt3+\sqrt3$  a s v
b) $\sqrt6+\sqrt6$  a s v
c) $\sqrt5+\sqrt5+\sqrt5$  a s v
d) $\sqrt{11}+\sqrt{11}+\sqrt{11}+\sqrt{11}$  a s v
e) $2\sqrt{13}+\sqrt{13}$  a s v
f) $3\sqrt{22}+2\sqrt{22}$  a s v
g) $5\sqrt{7}+3\times\sqrt{7}$  a s v
h) $13\times\sqrt{39}+2\times\sqrt{39}+\sqrt{39}$  a s v


Question 10


Simplify

a) $2\sqrt3-\sqrt3$  a s v
b) $5\sqrt{15}-\sqrt{15}$  a s v
c) $10\sqrt{21}-2\sqrt{21}$  a s v
d) $15\sqrt{15}-5\times\sqrt{15}$  a s v
e) $11\times\sqrt{43}-11\sqrt{43}$  a s v
f) $92\times\sqrt{94}-100\sqrt{94}$  a s v
g) $22\sqrt4-10\times\sqrt4$  a s v
h) $\sqrt{14}-2\sqrt{14}-33\times\sqrt{14}$  a s v


Question 11


Simplify

a) $\sqrt3\times\sqrt3+\sqrt5$  a s v
b) $\left(\sqrt{19}\right)^2+\sqrt{19}$  a s v
c) $\left(\sqrt{7}\right)^2+\left(\sqrt{7}\right)^4$  a s v
d) $\left(\sqrt{3}\right)^3$  a s v
e) $\left(\sqrt{11}\right)^3$  a s v
f) $\left(\sqrt{2}\right)^5$  a s v
g) $\sqrt6\times5\times\sqrt6\times3$  a s v
h) $\left(\sqrt{10}\right)^2\times5\times\sqrt{10}\times\sqrt9$  a s v