Question

Simplify the following expressions:

`(2sqrt5 + 3sqrt2)^2`

Answer 1

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

`(2sqrt5 + 3sqrt2)^2`

`∴ (2sqrt5 + 3sqrt2)^2 = (2sqrt5)^2 + (3sqrt2)^2 + 2 xx 2sqrt5 xx 3 sqrt2`

`= 2sqrt5 xx 2sqrt5 + 3sqrt2 xx 3sqrt2 + 2 xx 2sqrt5 xx 3sqrt2`

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

`= 4(5^2)^(1/2) + 9(2^2)^(1/2) + 12sqrt10`

`= 4 xx 5^1 + 9 xx 2^1 + 12sqrt10`

` = 20 + 18 + 12sqrt10`

`= 38 + 12sqrt10`

Hence the value of expression is `38 + 12sqrt10`