Simplify square root of 400i^8j^4k^6

$\sqrt{400 i^{8} j^{4} k^{6}}$

Step 1

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

$\sqrt{400 {(i^{4})}^{2} j^{4} k^{6}}$

Step 2

Rewrite $i^{4}$ as $1$ .

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$\sqrt{400 {({(i^{2})}^{2})}^{2} j^{4} k^{6}}$

Rewrite $i^{2}$ as $- 1$ .

$\sqrt{400 {({(- 1)}^{2})}^{2} j^{4} k^{6}}$

Raise $- 1$ to the power of $2$ .

$\sqrt{400 \cdot 1^{2} j^{4} k^{6}}$

Step 3

Simplify the expression.

One to any power is one.

$\sqrt{400 \cdot 1 j^{4} k^{6}}$

Multiply $400$ by $1$ .

$\sqrt{400 j^{4} k^{6}}$

Step 4

Rewrite $400 j^{4} k^{6}$ as ${(20 j^{2} k^{3})}^{2}$ .

$\sqrt{{(20 j^{2} k^{3})}^{2}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$20 j^{2} k^{3}$