Simplify the Radical Expression square root of 4r^8g^1p^3

$\sqrt{4 r^{8} g^{1} p^{3}}$

Step 1

Simplify.

$\sqrt{4 r^{8} g p^{3}}$

Step 2

Rewrite $4 r^{8} g p^{3}$ as ${(2 r^{4} p)}^{2} (g p)$ .

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} r^{8} g p^{3}}$

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

$\sqrt{2^{2} {(r^{4})}^{2} g p^{3}}$

Factor out $p^{2}$ .

$\sqrt{2^{2} {(r^{4})}^{2} g (p^{2} p)}$

Move $g$ .

$\sqrt{2^{2} {(r^{4})}^{2} p^{2} g p}$

Rewrite $2^{2} {(r^{4})}^{2} p^{2}$ as ${(2 r^{4} p)}^{2}$ .

$\sqrt{{(2 r^{4} p)}^{2} g p}$

Add parentheses.

$\sqrt{{(2 r^{4} p)}^{2} (g p)}$

Step 3

Pull terms out from under the radical.

$| 2 r^{4} p | \sqrt{g p}$

Step 4

Remove non-negative terms from the absolute value.

$2 r^{4} | p | \sqrt{g p}$