# Number - Surds Between Whole Numbers

**Question 1**

Follow the steps

a) Write a list of the first $5$ square numbers

a
$1,4,9,16,25$

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b) Find $\left(\sqrt5\right)^2$

a
$5$

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c) Which square numbers is $\left(\sqrt5\right)^2$ between?

a
$4$ and $9$

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d) Therefore which whole numbers is $\sqrt5$ between?

a
$2$ and $3$

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**Question 2**

Follow the steps

a) Write a list of the first $10$ square numbers

a
$1,4,9,16,25,36,49,64,81,100$

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b) Find $\left(\sqrt{52}\right)^2$

a
$52$

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c) Which square numbers is $\left(\sqrt{52}\right)^2$ between?

a
$49$ and $64$

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d) Therefore which whole numbers is $\sqrt{52}$ between?

a
$7$ and $8$

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**Question 3**

Use the method in the previous two questions to find which two whole numbers the following are in between

a) $\sqrt{11}$

a
$3$ and $4$

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b) $\sqrt{23}$

a
$4$ and $5$

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c) $\sqrt{43}$

a
$6$ and $7$

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d) $\sqrt{89}$

a
$9$ and $10$

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e) $\sqrt{68}$

a
$8$ and $9$

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f) $\sqrt{54}$

a
$7$ and $8$

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g) $\sqrt{40}$

a
$6$ and $7$

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h) $\sqrt{32}$

a
$5$ and $6$

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**Question 4**

Find which two whole numbers the following are in between

a) $\sqrt{101}$

a
$10$ and $11$

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b) $\sqrt{125}$

a
$11$ and $12$

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c) $\sqrt{200}$

a
$14$ and $15$

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d) $\sqrt{168}$

a
$12$ and $13$

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e) $\sqrt{268}$

a
$16$ and $17$

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f) $\sqrt{399}$

a
$19$ and $20$

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g) $\sqrt{901}$

a
$30$ and $31$

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h) $\sqrt{9998}$

a
$99$ and $10$

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**Question 5**

Are the following statements true or false?

a) $1<\sqrt{3}<2$

a
True

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b) $3<\sqrt{7}<4$

a
False

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c) $3\le\sqrt{10}\le4$

a
True

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d) $5<\sqrt{28}<6$

a
True

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e) $5>\sqrt{18}>4$

a
True

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f) $10\ge\sqrt{77}\ge9$

a
False

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g) $11>\sqrt{101}<8$

a
False

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h) $4\le\sqrt{83}\ge9$

a
True

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**Question 1**

Follow the steps

a) Write a list of the first $5$ square numbers

b) Find $\left(\sqrt5\right)^2$

c) Which square numbers is $\left(\sqrt5\right)^2$ between?

d) Therefore which whole numbers is $\sqrt5$ between?

**Question 2**

Follow the steps

a) Write a list of the first $10$ square numbers

b) Find $\left(\sqrt{52}\right)^2$

c) Which square numbers is $\left(\sqrt{52}\right)^2$ between?

d) Therefore which whole numbers is $\sqrt{52}$ between?

**Question 3**

Use the method in the previous two questions to find which two whole numbers the following are in between

a) $\sqrt{11}$

b) $\sqrt{23}$

c) $\sqrt{43}$

d) $\sqrt{89}$

e) $\sqrt{68}$

f) $\sqrt{54}$

g) $\sqrt{40}$

h) $\sqrt{32}$

**Question 4**

Find which two whole numbers the following are in between

a) $\sqrt{101}$

b) $\sqrt{125}$

c) $\sqrt{200}$

d) $\sqrt{168}$

e) $\sqrt{268}$

f) $\sqrt{399}$

g) $\sqrt{901}$

h) $\sqrt{9998}$

**Question 5**

Are the following statements true or false?

a) $1<\sqrt{3}<2$

b) $3<\sqrt{7}<4$

c) $3\le\sqrt{10}\le4$

d) $5<\sqrt{28}<6$

e) $5>\sqrt{18}>4$

f) $10\ge\sqrt{77}\ge9$

g) $11>\sqrt{101}<8$

h) $4\le\sqrt{83}\ge9$

__Answers__

**Question 1**

a) $1,4,9,16,25$

b) $5$

c) $4$ and $9$

d) $2$ and $3$

**Question 2**

a) $1,4,9,16,25,36,49,64,81,100$

b) $52$

c) $49$ and $64$

d) $7$ and $8$

**Question 3**

a) $3$ and $4$

b) $4$ and $5$

c) $6$ and $7$

d) $9$ and $10$

e) $8$ and $9$

f) $7$ and $8$

g) $6$ and $7$

h) $5$ and $6$

**Question 4**

a) $10$ and $11$

b) $11$ and $12$

c) $14$ and $15$

d) $12$ and $13$

e) $16$ and $17$

f) $19$ and $20$

g) $30$ and $31$

h) $99$ and $10$

**Question 5**

a) True

b) False

c) True

d) True

e) True

f) False

g) False

h) True

**Question 1**

Follow the steps

a) Write a list of the first $5$ square numbers

b) Find $\left(\sqrt5\right)^2$

c) Which square numbers is $\left(\sqrt5\right)^2$ between?

d) Therefore which whole numbers is $\sqrt5$ between?

**Question 2**

Follow the steps

a) Write a list of the first $10$ square numbers

b) Find $\left(\sqrt{52}\right)^2$

c) Which square numbers is $\left(\sqrt{52}\right)^2$ between?

d) Therefore which whole numbers is $\sqrt{52}$ between?

**Question 3**

Use the method in the previous two questions to find which two whole numbers the following are in between

a) $\sqrt{11}$

b) $\sqrt{23}$

c) $\sqrt{43}$

d) $\sqrt{89}$

e) $\sqrt{68}$

f) $\sqrt{54}$

g) $\sqrt{40}$

h) $\sqrt{32}$

**Question 4**

Find which two whole numbers the following are in between

a) $\sqrt{101}$

b) $\sqrt{125}$

c) $\sqrt{200}$

d) $\sqrt{168}$

e) $\sqrt{268}$

f) $\sqrt{399}$

g) $\sqrt{901}$

h) $\sqrt{9998}$

**Question 5**

Are the following statements true or false?

a) $1<\sqrt{3}<2$

b) $3<\sqrt{7}<4$

c) $3\le\sqrt{10}\le4$

d) $5<\sqrt{28}<6$

e) $5>\sqrt{18}>4$

f) $10\ge\sqrt{77}\ge9$

g) $11>\sqrt{101}<8$

h) $4\le\sqrt{83}\ge9$

__Answers__

**Question 1**

a) $1,4,9,16,25$

b) $5$

c) $4$ and $9$

d) $2$ and $3$

**Question 2**

a) $1,4,9,16,25,36,49,64,81,100$

b) $52$

c) $49$ and $64$

d) $7$ and $8$

**Question 3**

a) $3$ and $4$

b) $4$ and $5$

c) $6$ and $7$

d) $9$ and $10$

e) $8$ and $9$

f) $7$ and $8$

g) $6$ and $7$

h) $5$ and $6$

**Question 4**

a) $10$ and $11$

b) $11$ and $12$

c) $14$ and $15$

d) $12$ and $13$

e) $16$ and $17$

f) $19$ and $20$

g) $30$ and $31$

h) $99$ and $10$

**Question 5**

a) True

b) False

c) True

d) True

e) True

f) False

g) False

h) True

__Solutions__

**Question 1**

a)

b)

c)

d)

**Question 2**

a)

b)

c)

d)

**Question 3**

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b)

c)

d)

e)

f)

g)

h)

**Question 4**

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b)

c)

d)

e)

f)

g)

h)

**Question 5**

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b)

c)

d)

e)

f)

g)

h)