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Maths Quiz - Level 3-4 Algebra - Square Roots (Questions)

Learn square roots in KS3 algebra. Find roots of perfect squares, estimate others, and use Pythagoras to connect squares, roots, and right-angled triangles.

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Fascinating Fact:

For example, if one side of a triangle is 3 and another is 4, the hypotenuse is √(3² + 4²) = √25 = 5.

In KS3 Maths, square roots undo squaring. You’ll recognise perfect squares (like 1, 4, 9, 16), estimate roots of other numbers, and apply Pythagoras’ theorem to right-angled triangles using squares and roots.

Key Terms

Square root: A value that, when multiplied by itself, gives the original number; the principal root is the non-negative one (e.g. √36 = 6).
Perfect square: An integer that is a whole-number square, such as 25 = 5² or 64 = 8².
Surd: A root that cannot be written as a whole number, like √2 or √7.

Frequently Asked Questions (Click to see answers)

What does the square root symbol mean in KS3 maths?

The symbol √ means “square root”. For example, √49 = 7 because 7 × 7 = 49. The principal square root is always the non-negative value.

How do I simplify a square root like √50?

Split into a perfect square and the rest: √50 = √(25 × 2) = 5√2. This is called simplifying a surd.

Can a negative number have a square root?

Not in the real numbers you use at KS3. Negative numbers do not have real square roots because no real number squared gives a negative result.

Try These Related Quizzes

1.

The √ sign is referred to as what?

[ ]	Square
[ ]	Squared
[ ]	Square root
[ ]	Square rooted

2.

What is the square root of 16?

[ ]	2 or -2
[ ]	4 or -4
[ ]	6 or -6
[ ]	8 or -8

3.

What is the square root of 81?

[ ]	3 or -3
[ ]	6 or -6
[ ]	9 or -9
[ ]	12 or -12

4.

Which of these numbers has a whole number as a square root?

[ ]	30
[ ]	32
[ ]	34
[ ]	36

5.

Which of these figures does not have a whole number as a square root?

[ ]	25
[ ]	35
[ ]	49
[ ]	64

6.

What is the quickest way to find the square root of 8?

[ ]	Divide 8 by 2
[ ]	Multiply 8 x 2
[ ]	Take 2 from 8
[ ]	Use a calculator

7.

What is the square of 9?

[ ]	3
[ ]	6
[ ]	9
[ ]	81

8.

What is the square root of 100?

[ ]	2 or -2
[ ]	10 or -10
[ ]	25 or -15
[ ]	50 or -50

9.

You are given the two numbers '9 squared' and '81'. How do they relate to each other?

[ ]	81 is the larger number
[ ]	9 squared is the larger number
[ ]	They are both the same
[ ]	They are in no way related

10.

You are given the two numbers '3 squared' and 'the square root of 100'. How do they relate to each other?

[ ]	3 squared is the larger number
[ ]	The square root of 100 is the larger number
[ ]	They are both the same
[ ]	There is no way of telling

You can find more about this topic by visiting BBC Bitesize - Power and roots

Maths Quiz - Level 3-4 Algebra - Square Roots (Answers)

1.

The √ sign is referred to as what?

[ ]	Square
[ ]	Squared
[x]	Square root
[ ]	Square rooted

It's important you get to know what the square root sign looks like

2.

What is the square root of 16?

[ ]	2 or -2
[x]	4 or -4
[ ]	6 or -6
[ ]	8 or -8

Both 4 x 4 and -4 x -4 = 16

3.

What is the square root of 81?

[ ]	3 or -3
[ ]	6 or -6
[x]	9 or -9
[ ]	12 or -12

9 x 9 = 81 AND -9 x -9 = 81

4.

Which of these numbers has a whole number as a square root?

[ ]	30
[ ]	32
[ ]	34
[x]	36

6 x 6 = 36

5.

Which of these figures does not have a whole number as a square root?

[ ]	25
[x]	35
[ ]	49
[ ]	64

The square root of 35 is 5.916079783099616

6.

What is the quickest way to find the square root of 8?

[ ]	Divide 8 by 2
[ ]	Multiply 8 x 2
[ ]	Take 2 from 8
[x]	Use a calculator

Some square roots are not whole numbers and can be very difficult to work out. The square root of 8 is approximately 2.828427. We used a calculator to find out!

7.

What is the square of 9?

[ ]	3
[ ]	6
[ ]	9
[x]	81

Did you spot that we asked for the 'square' and NOT the 'square root'?

8.

What is the square root of 100?

[ ]	2 or -2
[x]	10 or -10
[ ]	25 or -15
[ ]	50 or -50

Minus numbers multiplied by themselves always give a positive answer. So, strange as it seems, -10 x -10 = 100

9.

You are given the two numbers '9 squared' and '81'. How do they relate to each other?

[ ]	81 is the larger number
[ ]	9 squared is the larger number
[x]	They are both the same
[ ]	They are in no way related

9 x 9 = 81

10.

You are given the two numbers '3 squared' and 'the square root of 100'. How do they relate to each other?

[ ]	3 squared is the larger number
[ ]	The square root of 100 is the larger number
[ ]	They are both the same
[x]	There is no way of telling

The square root of 100 could be either 10 or -10 and we have no way of knowing which square root the question requires!