Maths Quiz - Level 5-6 Numbers - Roots (Answers)
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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You can find more about this topic by visiting BBC Bitesize - Roots
The square root of 125 is 11.18 to two decimal places.
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202 = 400; 212 = 441. √425 = 20.61552813.......
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Since 162 = 256, 163 must be bigger and 263 or 363 will be bigger still, so 6 is the only sensible answer
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√169 = 13
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∛1,000 = 10
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To find the square root of a power number you divide the index by 2. √(54) = 52
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The square root of a product is the product of the square roots. √64 x √144 = 8 x 12
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To find the cube root of a power number you divide the index by 3. ∛(79) = 73
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9 x 16 = 144. √144 = 12
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∛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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