Simplify square root of 600a^9b^7c^11

$\sqrt{600 a^{9} b^{7} c^{11}}$

Step 1

Rewrite $600 a^{9} b^{7} c^{11}$ as ${(10 a^{4} b^{3} c^{5})}^{2} \cdot (6 a b c)$ .

Factor $100$ out of $600$ .

$\sqrt{100 (6) a^{9} b^{7} c^{11}}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 6 a^{9} b^{7} c^{11}}$

Factor out $a^{8}$ .

$\sqrt{10^{2} \cdot 6 (a^{8} a) b^{7} c^{11}}$

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

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2} a) b^{7} c^{11}}$

Factor out $b^{6}$ .

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2} a) (b^{6} b) c^{11}}$

Rewrite $b^{6}$ as ${(b^{3})}^{2}$ .

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2} a) ({(b^{3})}^{2} b) c^{11}}$

Factor out $c^{10}$ .

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2} a) ({(b^{3})}^{2} b) (c^{10} c)}$

Rewrite $c^{10}$ as ${(c^{5})}^{2}$ .

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2} a) ({(b^{3})}^{2} b) ({(c^{5})}^{2} c)}$

Move $b$ .

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2} a) ({(b^{3})}^{2}) {(c^{5})}^{2} b c}$

Move $a$ .

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2}) ({(b^{3})}^{2}) {(c^{5})}^{2} a b c}$

Move $6$ .

$\sqrt{(10^{2} ({(a^{4})}^{2})) ({(b^{3})}^{2}) {(c^{5})}^{2} \cdot 6 a b c}$

Rewrite $((10^{2} ({(a^{4})}^{2})) ({(b^{3})}^{2})) {(c^{5})}^{2}$ as ${(10 a^{4} b^{3} c^{5})}^{2}$ .

$\sqrt{{(10 a^{4} b^{3} c^{5})}^{2} \cdot 6 a b c}$

Add parentheses.

$\sqrt{{(10 a^{4} b^{3} c^{5})}^{2} \cdot 6 a (b c)}$

Add parentheses.

$\sqrt{{(10 a^{4} b^{3} c^{5})}^{2} \cdot 6 (a (b c))}$

Add parentheses.

$\sqrt{{(10 a^{4} b^{3} c^{5})}^{2} \cdot (6 a b c)}$

Step 2

Pull terms out from under the radical.

$10 a^{4} b^{3} c^{5} \sqrt{6 a b c}$