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Maths Quiz - Level 5-6 Numbers - Roots (Questions)

Roots undo powers. Learn square roots to find side lengths, solve equations, and estimate values between perfect squares.

Fascinating Fact:

Architects use square roots to calculate diagonal lengths. A square floor 4 m wide has a diagonal of √(4² + 4²) = √32 ≈ 5.66 m.

In KS3 Maths, you will use roots to reverse powers and to solve practical problems. Square roots help find missing lengths, check solutions, and estimate values between perfect squares.

Key Terms

  • Square root: A number which, when multiplied by itself, gives the original number. For example, the square root of 25 is 5.
  • Perfect square: A whole number made by squaring another whole number, like 1, 4, 9, 16, 25.
  • Radical sign: The symbol √ used to show a root, as in √36 = 6.

Frequently Asked Questions (Click to see answers)

What is a square root in KS3 Maths?

A square root is a number that multiplies by itself to make another number. For example, 7×7 = 49, so the square root of 49 is 7.

How can I estimate a square root without a calculator?

Find the two nearest perfect squares and interpolate. For example, √50 is between √49 = 7 and √64 = 8, so it is a little more than 7.

What is the difference between squares and square roots?

Squaring multiplies a number by itself, like 6² = 36. A square root reverses this process, so √36 = 6.

Try These Related Quizzes

1. Which of these is not a way of writing the square root of 625?
[ ] 25
[ ] 52
[ ] √125
[ ] 6251⁄5
2. The square root of 425 lies between .......
[ ] 19 and 20
[ ] 20 and 21
[ ] 21 and 22
[ ] 23 and 24
3. The cube root of 216 is .......
[ ] 6
[ ] 16
[ ] 26
[ ] 36
4. A square of area 169 cm2 has side length .......
[ ] 43 cm
[ ] 33 cm
[ ] 23 cm
[ ] 13 cm
5. A cube of volume 1,000 cm3 has side length .......
[ ] 1 cm
[ ] 10 cm
[ ] 100 cm
[ ] 1 m
6. What is the square root of 54?
[ ] 15
[ ] 25
[ ] 125
[ ] 250
7. What is the square root of 64 x 144?
[ ] 96
[ ] 72
[ ] 60
[ ] 48
8. What is the cube root of 79?
[ ] 49
[ ] 147
[ ] 343
[ ] 560
9. The square with the same area as a rectangle measuring 9 cm by 16 cm has side length .......
[ ] 6 cm
[ ] 9 cm
[ ] 12 cm
[ ] 15 cm
10. What is the total surface area of a cube which has a volume of 729 cm3?
[ ] 54 cm2
[ ] 81 cm2
[ ] 360 cm2
[ ] 486 cm2

You can find more about this topic by visiting BBC Bitesize - Roots

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Maths Quiz - Level 5-6 Numbers - Roots (Answers)
1. Which of these is not a way of writing the square root of 625?
[ ] 25
[ ] 52
[x] √125
[ ] 6251⁄5
The square root of 125 is 11.18 to two decimal places.
2. The square root of 425 lies between .......
[ ] 19 and 20
[x] 20 and 21
[ ] 21 and 22
[ ] 23 and 24
202 = 400; 212 = 441. ?425 = 20.61552813.......
3. The cube root of 216 is .......
[x] 6
[ ] 16
[ ] 26
[ ] 36
Since 162 = 256, 163 must be bigger and 263 or 363 will be bigger still, so 6 is the only sensible answer
4. A square of area 169 cm2 has side length .......
[ ] 43 cm
[ ] 33 cm
[ ] 23 cm
[x] 13 cm
?169 = 13
5. A cube of volume 1,000 cm3 has side length .......
[ ] 1 cm
[x] 10 cm
[ ] 100 cm
[ ] 1 m
?1,000 = 10
6. What is the square root of 54?
[ ] 15
[x] 25
[ ] 125
[ ] 250
To find the square root of a power number you divide the index by 2. ?(54) = 52
7. What is the square root of 64 x 144?
[x] 96
[ ] 72
[ ] 60
[ ] 48
The square root of a product is the product of the square roots. ?64 x ?144 = 8 x 12
8. What is the cube root of 79?
[ ] 49
[ ] 147
[x] 343
[ ] 560
To find the cube root of a power number you divide the index by 3. ?(79) = 73
9. The square with the same area as a rectangle measuring 9 cm by 16 cm has side length .......
[ ] 6 cm
[ ] 9 cm
[x] 12 cm
[ ] 15 cm
9 x 16 = 144. ?144 = 12
10. What is the total surface area of a cube which has a volume of 729 cm3?
[ ] 54 cm2
[ ] 81 cm2
[ ] 360 cm2
[x] 486 cm2
?729 = 9 so each square face has an area of 81 cm2. A cube has six square faces; 6 x 81 = 486
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