Simplify the Radical Expression square root of 72a^3b^4c^5

$\sqrt{72 a^{3} b^{4} c^{5}}$

Step 1

Rewrite $72 a^{3} b^{4} c^{5}$ as ${(6 a b^{2} c^{2})}^{2} \cdot (2 a c)$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2) a^{3} b^{4} c^{5}}$

Rewrite $36$ as $6^{2}$ .

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

Factor out $a^{2}$ .

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

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

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

Factor out $c^{4}$ .

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

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

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

Move $a$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$| 6 a b^{2} c^{2} | \sqrt{2 a c}$

Step 3

Remove non-negative terms from the absolute value.

$6 b^{2} c^{2} | a | \sqrt{2 a c}$