 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..

1.
What is the square root of 64 x 144?
96
72
60
48
The square root of a product is the product of the square roots. √64 x √144 = 8 x 12
2.
The square root of 425 lies between .......
19 and 20
20 and 21
21 and 22
23 and 24
202 = 400; 212 = 441. √425 = 20.61552813.......
3.
What is the total surface area of a cube which has a volume of 729 cm3?
54 cm2
81 cm2
360 cm2
486 cm2
∛729 = 9 so each square face has an area of 81 cm2. A cube has six square faces; 6 x 81 = 486
4.
What is the cube root of 79?
49
147
343
560
To find the cube root of a power number you divide the index by 3. ∛(79) = 73
5.
A square of area 169 cm2 has side length .......
43 cm
33 cm
23 cm
13 cm
√169 = 13
6.
What is the square root of 54?
15
25
125
250
To find the square root of a power number you divide the index by 2. √(54) = 52
7.
A cube of volume 1,000 cm3 has side length .......
1 cm
10 cm
100 cm
1 m
∛1,000 = 10
8.
Which of these is not a way of writing the square root of 625?
25
52
√125
6251⁄5
The square root of 125 is 11.18 to two decimal places.
9.
The cube root of 216 is .......
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
10.
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
9 x 16 = 144. √144 = 12
Author:  Frank Evans