Question

How do you simplify `(4[sqrt5] )/( 7[sqrt2] - 7[sqrt5])`?

Answer 1

`(4sqrt5)/(7sqrt2-7sqrt5)=-(20+4sqrt10)/21`

Explanation:

`(4sqrt5)/(7sqrt2-7sqrt5)=(4sqrt5)/(7(sqrt2-sqrt5))`

Now multiplying numerator and denominator by `(sqrt2-sqrt5)`, which is conjugate of denominator, we get

`(4sqrt5)/(7(sqrt2-sqrt5))xx(sqrt2+sqrt5)/(sqrt2+sqrt5)`

= `(4sqrt5(sqrt2+sqrt5))/(7(sqrt2-sqrt5)(sqrt2+sqrt5))`

= `(4sqrt10+4*5)/(7(2-5))`

= `(20+4sqrt10)/(7*(-3))`

= `-(20+4sqrt10)/21`