Basic Math Examples

$\frac{1}{2} \cdot \sqrt{108 a^{5} c^{7}}$

Step 1

Rewrite $108 a^{5} c^{7}$ as ${(6 a^{2} c^{3})}^{2} \cdot (3 a c)$ .

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Step 1.1

Factor $36$ out of $108$ .

$\frac{1}{2} \cdot \sqrt{36 (3) a^{5} c^{7}}$

Step 1.2

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

$\frac{1}{2} \cdot \sqrt{6^{2} \cdot 3 a^{5} c^{7}}$

Step 1.3

Factor out $a^{4}$ .

$\frac{1}{2} \cdot \sqrt{6^{2} \cdot 3 (a^{4} a) c^{7}}$

Step 1.4

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

$\frac{1}{2} \cdot \sqrt{6^{2} \cdot 3 ({(a^{2})}^{2} a) c^{7}}$

Step 1.5

Factor out $c^{6}$ .

$\frac{1}{2} \cdot \sqrt{6^{2} \cdot 3 ({(a^{2})}^{2} a) (c^{6} c)}$

Step 1.6

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

$\frac{1}{2} \cdot \sqrt{6^{2} \cdot 3 ({(a^{2})}^{2} a) ({(c^{3})}^{2} c)}$

Step 1.7

Move $a$ .

$\frac{1}{2} \cdot \sqrt{6^{2} \cdot 3 ({(a^{2})}^{2}) {(c^{3})}^{2} a c}$

Step 1.8

Move $3$ .

$\frac{1}{2} \cdot \sqrt{(6^{2} ({(a^{2})}^{2})) {(c^{3})}^{2} \cdot 3 a c}$

Step 1.9

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

$\frac{1}{2} \cdot \sqrt{{(6 a^{2} c^{3})}^{2} \cdot 3 a c}$

Step 1.10

Add parentheses.

$\frac{1}{2} \cdot \sqrt{{(6 a^{2} c^{3})}^{2} \cdot 3 (a c)}$

Step 1.11

Add parentheses.

$\frac{1}{2} \cdot \sqrt{{(6 a^{2} c^{3})}^{2} \cdot (3 a c)}$

Step 2

Pull terms out from under the radical.

$\frac{1}{2} \cdot (6 a^{2} c^{3} \sqrt{3 a c})$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $6 a^{2} c^{3} \sqrt{3 a c}$ .

$\frac{1}{2} \cdot (2 (3 a^{2} c^{3} \sqrt{3 a c}))$

Step 3.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 (3 a^{2} c^{3} \sqrt{3 a c}))$

Step 3.3

Rewrite the expression.

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