Algebra Examples

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

Step 1

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

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Step 1.1

Factor $16$ out of $80$ .

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

Step 1.2

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

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

Step 1.3

Factor out $b^{2}$ .

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

Step 1.4

Factor out $c^{2}$ .

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

Step 1.5

Move $b$ .

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

Step 1.6

Move $5$ .

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

Step 1.7

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

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

Step 1.8

Add parentheses.

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

Step 1.9

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.

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