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Square and Cube Numbers

Square and cube numbers are formed by multiplying a number by itself. When a number is multiplied by itself, we get a square of that number, and when a number is multiplied by itself thrice, we get its cube number.

Let’s look at square and cube numbers in greater detail:

 

Square numbers and Square roots

Square numbers are formed when we multiply a number by itself. For example, 5 x 5 = 25.

A square number is represented by the power of ‘2’. So 52 = 25. You will read it as “5 to the power of 2” or “5 square”.

The opposite of square is square root, and it is given by the symbol sqrt{.}

1. To find the square root of a number, we try and split the number into two same numbers and apply the square root.

For example –sqrt{225}

=  sqrt{15~*~15}

=  15

 

2. To find the square root of a number using its prime factors, take one factor from each pair of like factors, and multiply them to get the square root.

sqrt{176}  =  sqrt{14~*~14}

=  sqrt{7~*~2~*~7~*~2}

=  7 x 2  =  14

 

Cube and Cube roots

Cube numbers are formed by multiplying a number by itself thrice.

3 x 3 x 3 = 27. This is represented as 33 = 27, and you will read it as “3 to the power of 3” or “3 cube”. The opposite of cube is cube root, and it is given by the symbol root{3}{.}

1. To find the cube root, we find a number which multiplied by itself thrice give the number in the cube root.

Soroot{3}{125}

=  root{3}{5~*~5~*~5}  =  5

 

2. To find the cube root of a number using its prime factors, take one factor from each three like factors, and multiply them together to obtain the cube root.

For example –root{3}{512}  =  root{3}{8~*~8~*~8}

=  root{3}{(2*2*2)~*~(2*2*2)~*~(2*2*2)}

=  2 x 2 x 2  =  8

 

3. For larger numbers, you could attempt to split it into two, and work out the cube roots of these two numbers, and multiply them to get the cube root.

root{3}{27000}  =  root{3}{27}  x  root{3}{1000}

=  root{3}{3~*~3~*~3}   x   root{3}{10~*~10~*~10}

=  3 x 10  =  30