How do you simplify #3sqrt175#?

2 Answers
Mar 28, 2018

Answer:

Pull out as much of the value that's under the radical as possible. You'll find that the simplified version is #15sqrt(7)#

Explanation:

What I did was look for factors of the term underneath the radical (175) that were a perfect square.

I found that the largest term that fits the description is 25. I used that in the expression to simplify the expression:

#3sqrt(175)=3sqrt(25xx7)=3sqrt(25)sqrt(7)#

#3sqrt(25)sqrt(7)=3xx5sqrt(7)#

#color(red)(rArr 15sqrt(7))#

Mar 28, 2018

Answer:

15#sqrt7#

Explanation:

The number in the square root sign needs to be changed into two factors and one of these factors must be a square number.
175 = 7 x 25 so #sqrt175# = #sqrt7#x #sqrt25# or #sqrt7##sqrt25#

so #3 sqrt175# can be written 3#sqrt7##sqrt25#

as #sqrt25# = 5 then 3#sqrt7##sqrt25# = 15#sqrt7#