Question

Which expression is equal to 2−√ 32 ? 8i√2 −8√2 8√2i −8i√2

Answer 1

Answer:

A. $8i\sqrt{2}$

Step-by-step explanation:

We have been given a radical expression $2\sqrt{-32}$. We are asked to find equivalent expression to our given expression.

Using radical rule $\sqrt{-a}=\sqrt{-1}\cdot \sqrt{a}$, we can write $\sqrt{-32}$ as product of $\sqrt{-1}\cdot\sqrt{32}$.

$2\sqrt{-32}=2\cdot \sqrt{-1}\cdot\sqrt{32}$

Substitute $\sqrt{-1}=i$:

$2\sqrt{-32}=2i\cdot\sqrt{32}$

$2\sqrt{-32}=2i\cdot\sqrt{2\cdot 16}$

$2\sqrt{-32}=2i\cdot\sqrt{2\cdot 4^2}$

$2\sqrt{-32}=2*4i\cdot\sqrt{2}$

$2\sqrt{-32}=8i\sqrt{2}$

Therefore, the equivalent expression would be $8i\sqrt{2}$.

Answer 2

$2 \sqrt{-32}=2 \sqrt{-1*16*2} =2 \sqrt{-1} * \sqrt{16} * \sqrt{2} =2i*4* \sqrt{2} =8i \sqrt{2}$

I hope that helps!