Question

Simplify the following expressions:

`(sqrt3 + sqrt7)^2`

Answer 1

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

`(sqrt3 + sqrt7)^2`

`∴(sqrt3 + sqrt7)^2 = (sqrt3)^2 + (sqrt7)^2 + 2 xx sqrt3 xx sqrt7`

`= sqrt(3 xx 3) + sqrt(7 xx 7) + 2 xx  sqrt(3 xx 7)`

`= (3^2)^(1/2) + (7^2)^(1/2) + 2sqrt21`

`= 3^1+ 7^1 + 2sqrt21`

`= 10 + 2sqrt21`

Hence the value of expression is `10 + 2sqrt21`