Question

How do you simplify `(2sqrt5)/ (sqrt2 +5)`?

Answer 1

To simplify the expression, we need to make it's Denominator RATIONAL. And to do that, we multiply the numerator and the denominator with it's CONJUGATE.

The denominator is `sqrt2 + 5` which is the same as `5 + sqrt 2`

and it's CONJUGATE is `5 - sqrt2`

`(2sqrt5)/ (5+sqrt2) * (5 - sqrt 2)/(5 - sqrt 2)` (This keeps the Ratio unchanged)

`= ((2sqrt5) * (5 - sqrt 2))/(5^2 - (sqrt 2)^2)`

`= ((2sqrt5) * (5 - sqrt 2))/(25 - 2)`

`= ((2sqrt5) * (5 - sqrt 2))/(23)`

`= (10sqrt5 - 2sqrt 10)/(23)`

As the denominator 23 is RATIONAL, we have successfully simplified the expression.