Question

How do you simplify `sqrt14-sqrt(2/7)`?

Answer 1

`6/7 * sqrt(14)`

Explanation:

`sqrt(14) - sqrt(2/7)= sqrt(14) - sqrt(2)/sqrt(7) = sqrt(14) * sqrt(7)/sqrt(7) - sqrt(2) / sqrt(7)`

`= (sqrt(14) * sqrt(7) - sqrt(2))/sqrt(7) = (sqrt(2 * 7 * 7) - sqrt(2) ) / sqrt(7)`

`= (sqrt(2) * 7 - sqrt(2)) / sqrt(7) = (sqrt(2) * 6) / sqrt(7)`

If you would like to eliminate the radical in the denominator, you might want to take a few more steps:

`(sqrt(2) * 6) / sqrt(7) = (sqrt(2) * 6) / sqrt(7) * sqrt(7) / sqrt(7) = (sqrt(2) * sqrt( 7) * 6) / 7 = 6/7 * sqrt(14)`