Simplify the Radical Expression square root of 80a^2b^3c^3

$\sqrt{80 a^{2} b^{3} c^{3}}$

Step 1

Rewrite $80 a^{2} b^{3} c^{3}$ as ${(4 a b c)}^{2} \cdot (5 b c)$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5) a^{2} b^{3} c^{3}}$

Rewrite $16$ as $4^{2}$ .

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

Factor out $b^{2}$ .

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

Factor out $c^{2}$ .

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

Move $b$ .

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

Move $5$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$| 4 a b c | \sqrt{5 b c}$

Step 3

Remove non-negative terms from the absolute value.

$4 | a b c | \sqrt{5 b c}$