Question

How do you simplify `4sqrt(52x)+sqrt(117x)-2sqrt13`?

Answer 1

`=sqrt13(8sqrtx +3sqrtx-2)`

Explanation:

Write each value under the root as the product of the factors, then we can compare the terms.

`4sqrt(52x) + sqrt(117x) - 2sqrt13`

`=4sqrt(4xx13x) + sqrt(9xx13x) - 2sqrt13`

`=4sqrt4xxsqrt(13x) + sqrt9xxsqrt(13x) - 2sqrt13`

`=4 xx 2 color(red)(sqrt13)sqrtx +3color(red)(sqrt13)sqrtx-2color(red)(sqrt13)" "larr` common factor

`=color(red)(sqrt13)(8sqrtx +3sqrtx-2)`