Question

Which expression is equal to 2 sqrt -28


4 sqrt7i
-4 sqrt7
-4i sqrt7
4i sqrt 7

Answer 1

Which expression is equal to $2\sqrt{-28}$

Solution

Step 1:

We have to rewrite $\sqrt{-28}$ = $\sqrt{-1} \sqrt{28}$

$2\sqrt{-1} \sqrt{28}$

Step 2:

$\sqrt{-1}  = i$

Now plug in the above value in the step 1, we get

$2i\sqrt{28}$

We can write $\sqrt{28} = \sqrt{4} \sqrt{7} = 2\sqrt{7}$

Step 3:

Now, we plug in $\sqrt{28} = 2\sqrt{7}$ in the above expression , we get

$2i*2*\sqrt{7}$

Step 4:

Simplifying, we get

$4i\sqrt{7}$

Therefore, the answer is d) 4i sqrt 7