Simplify square root of 88m^3p^2r^5

$\sqrt{88 m^{3} p^{2} r^{5}}$

Step 1

Rewrite $88 m^{3} p^{2} r^{5}$ as ${(2 m p r^{2})}^{2} \cdot (22 m r)$ .

Factor $4$ out of $88$ .

$\sqrt{4 (22) m^{3} p^{2} r^{5}}$

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

$\sqrt{2^{2} \cdot 22 m^{3} p^{2} r^{5}}$

Factor out $m^{2}$ .

$\sqrt{2^{2} \cdot 22 (m^{2} m) p^{2} r^{5}}$

Factor out $r^{4}$ .

$\sqrt{2^{2} \cdot 22 (m^{2} m) p^{2} (r^{4} r)}$

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

$\sqrt{2^{2} \cdot 22 (m^{2} m) p^{2} ({(r^{2})}^{2} r)}$

Move $m$ .

$\sqrt{2^{2} \cdot 22 (m^{2}) p^{2} {(r^{2})}^{2} m r}$

Move $22$ .

$\sqrt{(2^{2} (m^{2})) p^{2} {(r^{2})}^{2} \cdot 22 m r}$

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

$\sqrt{{(2 m p r^{2})}^{2} \cdot 22 m r}$

Add parentheses.

$\sqrt{{(2 m p r^{2})}^{2} \cdot 22 (m r)}$

Add parentheses.

$\sqrt{{(2 m p r^{2})}^{2} \cdot (22 m r)}$

Step 2

Pull terms out from under the radical.

$2 m p r^{2} \sqrt{22 m r}$