Question

Simplify the following expressions:

`(sqrt5 - sqrt3)^2`

Answer 1

We know that `(a - b)^2 = a^2 + b^2 - 2ab`. We will use this property to simplify the expression

`(sqrt5 - sqrt3)`

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

`= sqrt5 xx sqrt5 + sqrt3 xx sqrt3 - 2 xx sqrt(5 xx 3)`

`= sqrt(5 xx 5) + sqrt(3 xx 3) -  2 xx sqrt(5 xx 3)`

`= (5^2)^(1/2) + (3^2)^(1/2) - 2sqrt15`

`= 5^1 + 3^1 - 2sqrt15`

`= 8 - 2sqrt15`

Hence the value of expression is `8 - 2sqrt15`