Question

Simplify the following expressions:

`(sqrt5 - 2)(sqrt3 - sqrt5)`

Answer 1

 We can simplify the expression `(sqrt5 - 2)(sqrt3 - sqrt5)` as

`(sqrt5 - 2)(sqrt3 - sqrt5) = sqrt5 xx sqrt3 - sqrt5 xx sqrt5 - 2 xx sqrt3 + 2 xx sqrt5`

`= sqrt15 - sqrt(5 xx 5) - 2sqrt3 + 2sqrt5`

`=sqrt15 - (5^2)^(1/2) - 2sqrt3 +2sqrt5`

`= sqrt15 - (5^2)^(1/2) - 2sqrt3 + 2sqrt5`

`= sqrt15 - 5^1 - 2sqrt3 + 2sqrt5`

Hence the value of the expression is `sqrt15 - 2sqrt3 + 2sqrt5 - 5`