Number - Surds Between Whole Numbers

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Question 1


Follow the steps

a) Write a list of the first $5$ square numbersa s v

b) Find $\left(\sqrt5\right)^2$a s v

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

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



Question 2


Follow the steps

a) Write a list of the first $10$ square numbersa s v

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

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

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



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 s v
b) $\sqrt{23}$a s v
c) $\sqrt{43}$a s v
d) $\sqrt{89}$a s v
e) $\sqrt{68}$a s v
f) $\sqrt{54}$a s v
g) $\sqrt{40}$a s v
h) $\sqrt{32}$a s v


Question 4


Find which two whole numbers the following are in between

a) $\sqrt{101}$a s v
b) $\sqrt{125}$a s v
c) $\sqrt{200}$a s v
d) $\sqrt{168}$a s v
e) $\sqrt{268}$a s v
f) $\sqrt{399}$a s v
g) $\sqrt{901}$a s v
h) $\sqrt{9998}$a s v


Question 5


Are the following statements true or false?

a) $1<\sqrt{3}<2$a s v
b) $3<\sqrt{7}<4$a s v
c) $3\le\sqrt{10}\le4$a s v
d) $5<\sqrt{28}<6$a s v
e) $5>\sqrt{18}>4$a s v
f) $10\ge\sqrt{77}\ge9$a s v
g) $11>\sqrt{101}<8$a s v
h) $4\le\sqrt{83}\ge9$a s v