Topics
1. Whole Numbers
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iGCSE (2021 Edition)

1.09 Roots of numbers

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[3]{1000} = 10

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}
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Outcomes

0580C1.1E

Identify and use rational and irrational numbers (e.g. π, sqrt(2) ).

0580C1.3A

Calculate with squares, square roots, cubes and cube roots.

0580E1.1E

Identify and use rational and irrational numbers (e.g. π, sqrt(2) ).

0580E1.3A

Calculate with squares, square roots, cubes and cube roots of numbers.

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