Question

question
express in simplest radical form.
$8\sqrt{2} + 8\sqrt{50}$

Explanation:

Step1: Simplify $\sqrt{50}$

We know that $50 = 25\times2$, and $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a\geq0,b\geq0$). So $\sqrt{50}=\sqrt{25\times2}=\sqrt{25}\times\sqrt{2}=5\sqrt{2}$.

Step2: Substitute back into the expression

The original expression is $8\sqrt{2}+8\sqrt{50}$. Substituting $\sqrt{50} = 5\sqrt{2}$, we get $8\sqrt{2}+8\times(5\sqrt{2})$.

Step3: Simplify the expression

First, calculate $8\times(5\sqrt{2}) = 40\sqrt{2}$. Then the expression becomes $8\sqrt{2}+40\sqrt{2}$. Since the terms have the same radical part, we can combine like terms: $(8 + 40)\sqrt{2}=48\sqrt{2}$.

Answer:

$48\sqrt{2}$