Factor out Square Roots

The square root is the radical form of the method that are used in the calculation mathematical problems. The symbol for the square root is meant by root √. This could be in the form to describe their nature of working with the square roots. There are numerous methods are available in the rooting, they are square (second) root `sqrt(x)` , cube (Third) root `root(3)(x)` up to nth root `root(n)(x)` .  Here we are going to see about how to factor out square roots and solved example problems based on the factor out square roots.

Some Examples for Square Root Operations:

`sqrt(x) xx sqrt(y)` =`sqrt(xy)`   [By the first property]
`xsqrty` = `sqrt(x^2y)`              [By the second property]
`sqrt(x/y)` = `sqrtx/sqrty`          [By the third property]


Steps to factor out square roots:

Get the values to find the factor out square root values.
Now check for the factors in the given square root. The factor should be in the squared form for factoring the value out of the root symbol.
The squared values are factor out from the square root symbol and
Write the calculated value in the correct form.

Factor out Square Roots - Example Problems:

Factor out square roots -  Problem 1:

Solve for factor out square root of 448

Solution:

Factoring out the square root of 448

`sqrt 448`

Finding factors by L Division method

2  |448

2  |224

2  |112

2  |56

2  |28

2  |14

7

The factor for the `sqrt(448)` is `sqrt(2^6xx7)`

=  ` sqrt(2^6 xx 7)`

= `8 sqrt 7`

The factor out value for the square root value of 448 is `8sqrt7`

Factor out square roots -  Problem 2:

Solve for factor out square root of 648

Solution:

Factoring out the square root of 648

`sqrt 648`

Finding factors by L Division method

2 |648

2 |324

2 |162

3 |81

3 |27

3 |9

3

The factor for the `sqrt(648)` is `sqrt(2^3xx 3^4)`

=  ` 2xx9 sqrt(2 )`

= `18 sqrt 2`
The factor out value for the square root value of 448 is `18sqrt2`


Factor out square roots -  Problem 2:

Solve for factor out square root of 528

Solution:

Factoring out the square root of 528

`sqrt 528`

Finding factors by L Division method

2 |528

2 |264

2 |132

2 |66

3 |33

11

The factor for the `sqrt(528)` is `sqrt(2^4xx 3 xx 11)`

=  ` 2sqrt(33)`
The factor out value for the square root value of 528 is ` 2sqrt33`