Topics
1. Number
topic badge
iGCSE (2021 Edition)

1.03 Square roots and cube roots

Lesson
Worksheet
Practice
Worksheet
Perfect squares
1

State whether the following numbers are perfect squares:

a
6
b
25
c
49
d
44
e
18
f
144
g
36
h
12
2

Evaluate the following:

a
4^{2}
b
7^{2}
c
9^{2}
d
12^{2}
e
9^{2} + 6
f
3^{2} + 7^{2}
g
7^{2} + 9^{2}
h
100^{2} + 10^{2}
i
7^{2} - 3^{2}
j
9^{2} - 8^{2}
k
12^{2} - 6^{2}
l
100^{2} - 10^{2}
3

Harry was working out 2^{2} \times 5^{2} and thought that he could simplify the expression using the fact that 2 \times 5 = 10.

a

Evaluate 2^{2} \times 5^{2}, by first expanding and evaluating each square.

b

Now, using the fact 2 \times 5 = 10, evaluate 10^{2}.

c

Is 2^{2} \times 5^{2} = \left( 2 \times 5\right)^{2} a true statement?

d

Calculate 4^{2} \times 2^{2} using the above method.

Square roots
4

Given that we know 5 \times 5 = 25. What is \sqrt{25}?

5

Evaluate the following:

a
\sqrt{4}
b
\sqrt{16}
c
\sqrt{121}
d
\sqrt{144} + \sqrt{64}
e
\sqrt{144} - \sqrt{64}
f
\sqrt{6^{2} + 8^{2}}
g
\sqrt{13^{2} - 12^{2}}
h
\sqrt{13^{2}} - \sqrt{12^{2}}
Higher roots
6

Are the following statements true or false?

a

\sqrt{64} = 8

b

\sqrt[3]{64} = 4

7

Evaluate the following:

a
\sqrt[3]{27}
b
\sqrt[3]{64}
c
\sqrt[3]{1000}
d
\sqrt[3]{343}
8

Evaluate the following:

a
\sqrt[4]{16}
b
\sqrt[4]{256}
c
\sqrt[5]{100\,000}
d
\sqrt[5]{32}
9

Solve x^{3} = 64.

10

Find the side length of a cube with a volume of 27\text{ cm}^3.

11

Evaluate the following:

a
\sqrt[3]{512} \times \sqrt[3]{64}
b
\sqrt[3]{64} \div \sqrt[3]{8}
c
\sqrt[3]{8} \times \sqrt[3]{1000}
d
\sqrt[3]{64} \div \sqrt{16}
e
6^2 \div \sqrt[3]{8}
f
\sqrt[3]{1000} \div \sqrt{100}
g
8^3 \div \sqrt[3]{64}
h
\sqrt[3]{125} \times \sqrt[5]{32} \div \sqrt[3]{8}
Sign up to access Worksheet
Get full access to our content with a Mathspace account
Book a Demo
Sign up for free

Outcomes

0607C1.4

Calculation of powers and roots.

0607E1.4

Calculation of powers and roots.

What is Mathspace

About Mathspace