Question

How do you simplify `3sqrt175`?

Answer 1

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))`

Answer 2

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`