Question

what is the following sum in simplest form?
$sqrt{8} + 3sqrt{2} + sqrt{32}$
options:
$9sqrt{2}$
$5sqrt{42}$
$3sqrt{8} + 3sqrt{2}$
$5sqrt{2} + sqrt{32}$

Explanation:

Step1: Simplify each radical

Simplify $\sqrt{8}$: $\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}$
Simplify $\sqrt{32}$: $\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$

Step2: Substitute back into the expression

The original expression is $\sqrt{8} + 3\sqrt{2} + \sqrt{32}$. Substituting the simplified radicals, we get:
$2\sqrt{2} + 3\sqrt{2} + 4\sqrt{2}$

Step3: Combine like terms

Combine the coefficients of $\sqrt{2}$:
$(2 + 3 + 4)\sqrt{2} = 9\sqrt{2}$

Answer:

$9\sqrt{2}$ (corresponding to the option with "9√2")