Question

select the correct answer.
what is this expression in simplified form?
√32 · 5√2
8
12
40
5√34

Explanation:

Step1: Simplify $\sqrt{32}$

We know that $32 = 16\times2$, so $\sqrt{32}=\sqrt{16\times2}$. By the property of square roots $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ (where $a = 16$ and $b = 2$), we get $\sqrt{16\times2}=\sqrt{16}\cdot\sqrt{2}=4\sqrt{2}$.

Step2: Multiply the two radical expressions

Now we have to multiply $4\sqrt{2}$ and $5\sqrt{2}$. When multiplying radical expressions of the form $a\sqrt{b}\cdot c\sqrt{d}$, we can use the property $(a\sqrt{b})\cdot(c\sqrt{d})=(a\times c)\times\sqrt{b\times d}$. So, $4\sqrt{2}\cdot5\sqrt{2}=(4\times5)\times\sqrt{2\times2}$.

Step3: Simplify the result

First, $4\times5 = 20$, and $\sqrt{2\times2}=\sqrt{4} = 2$. Then we multiply these two results: $20\times2=40$.

Answer:

40 (corresponding to the option "40")