Question

Can 6/(√5-√2) be simplified, and if so, how?

Answer 1

`2(√(5) +√(2))`

Explanation:

To simplift a radical expression like the one given, we first need to multiply the numerator and the denominator by the conjugate of the denominator, which is given by simply reversing the sign between the expression. So:

`(6)/(√(5)-√(2) ) * (√(5)+√(2) )/(√(5)+√(2) )`

Notive how the denominator is just a difference of squares. Simplifying, we are left with:

`(6(√(5) +√(2)))/(5-2) = (6(√(5) +√(2)))/(3) = 2(√(5) +√(2))`

And that's our answer!