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Level 3-4 Algebra - Square Roots
The square root of 49 can be 7 or -7.

Level 3-4 Algebra - Square Roots

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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(quiz starts below)

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 .
What is the square root of 16?
2 or -2
4 or -4
6 or -6
8 or -8
Both 4 x 4 and -4 x -4 = 16
2 .
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
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!
3 .
The √ sign is referred to as what?
Square
Squared
Square root
Square rooted
It's important you get to know what the square root sign looks like
4 .
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
The square root of 100 could be either 10 or -10 and we have no way of knowing which square root the question requires!
5 .
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
9 x 9 = 81
6 .
Which of these figures does not have a whole number as a square root?
25
35
49
64
The square root of 35 is 5.916079783099616
7 .
What is the square root of 100?
2 or -2
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
8 .
Which of these numbers has a whole number as a square root?
30
32
34
36
6 x 6 = 36
9 .
What is the square root of 81?
3 or -3
6 or -6
9 or -9
12 or -12
9 x 9 = 81 AND -9 x -9 = 81
10 .
What is the square of 9?
3
6
9
81
Did you spot that we asked for the 'square' and NOT the 'square root'?
You can find more about this topic by visiting BBC Bitesize - Power and roots

Author:  Frank Evans (Specialist 11 Plus Teacher and Tutor)
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