Question

Simplify the following square roots:


`√(32)`

`√(28)`

`√(12)`

Answer 1

They can not be simplified because they are not perfect squares.

Answer 2

Sqrt32 = 4
`√(2)`, Sqrt28 = 2
`√(7)`, Sqrt12 = 2
`√(3)`

Explanation:

Square root of 32:

First we find the prime factors of the number by making a factor tree.

32 splits into 8 and 4.

8 splits into 4 and 2

4 splits into 2 and 2

4 splits into 2 and 2

This becomes the square root of
`2^(2)` x
`2^(2)` x 2. It will simplify to:

4
`√(2)`

Square root of 28:

The prime factors of this number are:

2, and 2

This simplifies to 2
`√(7)`

Square root of 12:

The prime factors of this are:

3, 2, 2

This simplifies to:

2
`√(3)`