How do I simplify square roots?

Question

How do I simplify √75? Steps?

Answer 1

Simplifying is different than finding an approximation by simply punching buttons on your calculator and getting a decimal that you would have to round.

In order to simplify this particular problem, you would use the product rule: √ab = √a√b

In other words you want to break down the number under the root into factors, one of which should be a perfect square, so you can take the square root of all that you can and leave the remaining amount that can’t be broken down further under the square root symbol.

Here are the steps:



√75 = √(25)(3)

(this is advantageous since 25 is a perfect square and we will be able to take the square root of it once we break the root apart using the product property)



√(25)(3) = √(25)√((3) = 5√3

(5 is the square root of 25 and since 3 can not be factored further into any perfect square parts, this is considered simplest form.)

Answer 2

The first step is to break down 75 as a multiple of its factors, so

75 = 3 x 5 x 5



then take out the numbers which appear twice in the factors, so in the above case, it is 5



√75

= √3 x 5 x 5

= 5√3 x 5

=5√15

Answer 3

When the square root isn't obvious, factor.



√75 factors to √25x3



√25x3 = √25 x √3 = 5 x √3 or 5√3

Answer 4

"Solution: Given √75



=>√(5*5*3)



=> √(5²*3)



5 we will takeout of the bracket because we have 5 two times



=> 5√3"