Investigate Square and Cube Numbers and Their Roots

This activity is about square and cube numbers and their roots.  

All answers are positive.

 

 

Square numbers are what we get when we multiply a number by itself. 

Here's a reminder of the first five square numbers:

 

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

 

Square roots are the numbers we multiply to get a square number. 

So, 5 is the square root of 25.

 

Cube numbers are calculated by multiplying a number by itself, then by itself again!

Here's a reminder of the first three cube numbers:

 

 

So, we know that 5 x 5 x 5 = 125 

125 is a cube number.

Which means that 5 is the cube root of 125.

 

Let's try an example question.

 

Example

Tom takes 3 cubed and adds 2 squared. 

What number does he get?

 

Answer

3 cubed = 3 x 3 x 3 = 27

2 squared = 2 x 2 = 4

27 + 4 = 31

 

The answer is 31

 

Now let's try some questions about square and cube numbers, and their roots.