KS3 Maths Quiz
How good are you at roots? That is, mathematical roots not tree roots!

# Level 5-6 Numbers - Roots

So, KS3 Maths has made you familiar with square numbers and cube numbers. They are powers denoted by a 2 or a 3 above and to the right of another number. For example, 3 squared is 32 and 3 cubed is 33. But there is another side to squares and cubes - roots.

A number multiplied by itself creates its own square. The original number is called the square root of the new number. For example, the square root of 9 is 3 because 3 x 3 = 9. It's similar with cube roots. A number multiplied by itself twice creates a cube number. The original number is the cube root of this. For example, the cube root of 64 is 4 because 4 x 4 x 4 = 64. It's not easy to work out square or cube roots. It usually involves a great deal of trial and error - or a calculator!

It would be great if you could memorise the square and cube values of lower numbers. That would help you a lot but might take a considerable amount of time. In the meanwhile, try this quiz to get some practise with square and cube roots..

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1. A square of area 169 cm2 has side length .......
√169 = 13
2. A cube of volume 1,000 cm3 has side length .......
∛1,000 = 10
3. The square root of 425 lies between .......
202 = 400; 212 = 441. √425 = 20.61552813.......
4. Which of these is not a way of writing the square root of 625?
The square root of 125 is 11.18 to two decimal places.
5. The cube root of 216 is .......
Since 162 = 256, 163 must be bigger and 263 or 363 will be bigger still, so 6 is the only sensible answer
6. The square with the same area as a rectangle measuring 9 cm by 16 cm has side length .......
9 x 16 = 144. √44 = 12
7. What is the total surface area of a cube which has a volume of 729 cm3?
∛729 = 9 so each square face has an area of 81 cm2. A cube has six square faces; 6 x 81 = 486
8. What is the square root of 54?
To find the square root of a power number you divide the index by 2. √(54) = 52
9. What is the square root of 64 x 144?
The square root of a product is the product of the square roots. √64 x √144 = 8 x 12
10. What is the cube root of 79?
To find the cube root of a power number you divide the index by 3. ∛(79) = 73

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