Question

simplifying radicals
score: 2/5 penalty: none
question
express in simplest radical form.
√8
answer attempt 1 out of 3

Explanation:

Step1: Factor the radicand

We know that $8 = 4\times2$, and $4$ is a perfect square. So we can rewrite $\sqrt{8}$ as $\sqrt{4\times2}$.

Step2: Use the property of square roots

According to the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a\geq0$ and $b\geq0$), we have $\sqrt{4\times2}=\sqrt{4}\times\sqrt{2}$.

Step3: Simplify the perfect square root

Since $\sqrt{4} = 2$, then $\sqrt{4}\times\sqrt{2}=2\times\sqrt{2}=2\sqrt{2}$.

Answer:

$2\sqrt{2}$