How to Work out the Square Root and Cube Root of a Number?

First of all let’s take a look at square roots.

If you want to find a square root of a number then you need to look for a number when multiplied by itself to give the number that you are square rooting.

So if you have √a then ? × ? = a

Let’s cover a few questions:

Question 1

Work out √16 (this means the square root of 16)

Since 4 × 4 = 16 then the square root of 16 is 4.

Question 2

Work out √49

Since 7 × 7 = 49 then the square root of 49 is 7.

Question 3

Work out √225

Since 15 × 15 = 225 then the square root of 225 is 15.

Question 4

Work out √1

Since 1 × 1 = 1 then the square root of 1 is 1.

Question 5

Work out √144

Since 12 × 12 = 144 then the square root of 144 is 12.

Let’s now look at cube roots. This time you are looking for a number such that ? × ? × ? gives the number that you are cube rooting. Let’s go over a few questions of cube roots:

Question 6

Work out ³√27 (that is the cube root of 27)

So you are looking for a number such that ? × ? × ? = 27. The number that you looking for is 3 because 3 × 3 × 3 = 27 (3 × 3 = 9 so 9 × 3 = 27). Therefore the cube root of 27 is 3.

Question 7

Work out ³√8 (that is the cube root of 8)

So you are looking for a number such that ? × ? × ? = 8. The number that you looking for is 8 because 2 × 2 × 2 = 8 (2 × 2 = 4 so 4 × 2 = 8). Therefore the cube root of 8 is 2.

Question 8

Work out ³√64 (that is the cube root of 64)

So you are looking for a number such that ? × ? × ? = 64. The number that you looking for is 4 because 4 × 4 × 4 = 64 (4 × 4 = 16 so 16 × 4 = 64). Therefore the cube root of 64 is 4.

Question 9

Work out ³√125 (that is the cube root of 125)

So you are looking for a number such that ? × ? × ? = 125. The number that you looking for is 5 because 5 × 5 × 5 = 125 (5 × 5 = 25 so 25 × 5 = 125). Therefore the cube root of 125 is 5.

Question 10

Work out ³√-8 (that is the cube root of negative 8)

So you are looking for a number such that ? × ? × ? = -8. The number that you looking for is -2 because -2 × -2 × -2 = -8 (-2 × -2 = 4 so 4 × -2 = -8). Therefore the cube root of -8 is -2.

So to summarise if you are taking the square root of a number then you are looking for a number such that ? × ? = the number you are rooting. And if you are taking the cube root of a number then you are looking for a number such that ? × ? × ? = the number that you are cube rooting.

Sometimes you will find that you will not be able to square root a number in your head because the answer will be a decimal answer. In this case you will need to use a scientific calculator. On a Casio calculator the button is usually located near the top of the calculated and has a tick with a box underneath. So for example, to work out the square root of 21, then you will need to use the root key on your calculator to give 4.582575695, which you can round off to 4.58 to 2 decimal places. Again, you can check the answer by multiplying 4.58 by 4.58 to give 20.9764. Although there is a slight inaccuracy due to rounding off the numbers to two decimal places.

Similarly, with cube roots, there might not be an obvious answer so you will need a scientific calculator for tricky one. The cube root key on a Casio calculator is usually the second function key on the square root key. So for example, the cube root of 85 would not have an integer answer so you will need to use your calculator. The answer will be 4.396829672 or 4.40 rounded to 2 decimal places.