Simplify square root of 24a^16b^8c

$\sqrt{24 a^{16} b^{8} c}$

Step 1

Rewrite $24 a^{16} b^{8} c$ as ${(2 a^{8} b^{4})}^{2} \cdot (6 c)$ .

Factor $4$ out of $24$ .

$\sqrt{4 (6) a^{16} b^{8} c}$

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

$\sqrt{2^{2} \cdot 6 a^{16} b^{8} c}$

Rewrite $a^{16}$ as ${(a^{8})}^{2}$ .

$\sqrt{2^{2} \cdot 6 {(a^{8})}^{2} b^{8} c}$

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

$\sqrt{2^{2} \cdot 6 {(a^{8})}^{2} {(b^{4})}^{2} c}$

Move $6$ .

$\sqrt{2^{2} {(a^{8})}^{2} {(b^{4})}^{2} \cdot 6 c}$

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

$\sqrt{{(2 a^{8} b^{4})}^{2} \cdot 6 c}$

Add parentheses.

$\sqrt{{(2 a^{8} b^{4})}^{2} \cdot (6 c)}$

Step 2

Pull terms out from under the radical.

$2 a^{8} b^{4} \sqrt{6 c}$