Basic Math Examples

$9 \sqrt{8} \cdot \sqrt{6} \cdot \sqrt{3}$

Step 1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1

Factor $4$ out of $8$ .

$9 \sqrt{4 (2)} \cdot \sqrt{6} \cdot \sqrt{3}$

Step 1.2

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

$9 \sqrt{2^{2} \cdot 2} \cdot \sqrt{6} \cdot \sqrt{3}$

Step 2

Pull terms out from under the radical.

$9 (2 \sqrt{2}) \cdot \sqrt{6} \cdot \sqrt{3}$

Step 3

Multiply $2$ by $9$ .

$18 \sqrt{2} \cdot \sqrt{6} \cdot \sqrt{3}$

Step 4

Multiply $18 \sqrt{2} \sqrt{6}$ .

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Step 4.1

Combine using the product rule for radicals.

$18 \sqrt{6 \cdot 2} \cdot \sqrt{3}$

Step 4.2

Multiply $6$ by $2$ .

$18 \sqrt{12} \cdot \sqrt{3}$

Step 5

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 5.1

Factor $4$ out of $12$ .

$18 \sqrt{4 (3)} \cdot \sqrt{3}$

Step 5.2

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

$18 \sqrt{2^{2} \cdot 3} \cdot \sqrt{3}$

Step 6

Pull terms out from under the radical.

$18 (2 \sqrt{3}) \cdot \sqrt{3}$

Step 7

Multiply $2$ by $18$ .

$36 \sqrt{3} \cdot \sqrt{3}$

Step 8

Multiply $36 \sqrt{3} \sqrt{3}$ .

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Step 8.1

Raise $\sqrt{3}$ to the power of $1$ .

$36 ({\sqrt{3}}^{1} \sqrt{3})$

Step 8.2

Raise $\sqrt{3}$ to the power of $1$ .

$36 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Step 8.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$36 {\sqrt{3}}^{1 + 1}$

Step 8.4

Add $1$ and $1$ .

$36 {\sqrt{3}}^{2}$

Step 9

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 9.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$36 {(3^{\frac{1}{2}})}^{2}$

Step 9.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$36 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 9.3

Combine $\frac{1}{2}$ and $2$ .

$36 \cdot 3^{\frac{2}{2}}$

Step 9.4

Cancel the common factor of $2$ .

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Step 9.4.1

Cancel the common factor.

$36 \cdot 3^{\frac{2}{2}}$

Step 9.4.2

Rewrite the expression.

$36 \cdot 3^{1}$

Step 9.5

Evaluate the exponent.

$36 \cdot 3$

Step 10

Multiply $36$ by $3$ .

$108$