Algebra Examples

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

Step 1

Simplify.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Factor out $p^{2}$ .

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

Step 2.4

Move $g$ .

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

Step 2.5

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

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

Step 2.6

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.

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