Squares, Cubes and Roots


Squares, cubes and roots will crop up at some point in your maths exam.  If you take the time to study them they are really easy marks in your exam.  They can appear on either your calculator or non calculator paper.


Example Question

Work out the value of the following:

a)  112

b)  √81

c)  43

d)  3√27


Solution

a)  112 means "eleven squared".  To square a number mean to multiply it by itself.

So: 112 = 11 x 11 = 121

b)  
√81 means "the square root of eighty one".  To find a square root you must look for a number which when multiplied by itself gives the number in question.

So:
√81 = 9 (Since 9 x 9 = 81)

c)  
43 means "four cubed".  To cube a number you multiply it by itself and then by itself again.

So:  
43 = 4 x 4 x 4 = 64

d)  
3√27 means "the cube root of twenty seven".  To find a cube root you must look for a number which when you times it by itself and then itself again gives the number in question.

So:
3√27 = 3 (Since 3 x 3 x 3 = 27)

Before your exam it's a very good idea to remember the first few square and cube numbers so you don't waste time working them out in the exam.  Here are the key ones to remember:

x 1 2 3 4 5 6 7 8 9 10 11 12 13
x2 1 4 9 16 25 36 49 64 81 100 121 144 169
x3 1 8 27 64 125 -
- - - - - - -

It should not be necessary to remember more than the first 5 cube numbers.

Test Yourself!
Work out the answer to the following:

a)  72

 
b)  √144

 
c)  53

 
d)  3√8
 


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