Basic Math Examples

$(6 \sqrt{12} - \sqrt{12}) \sqrt{12}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $12$ .

$(6 \sqrt{4 (3)} - \sqrt{12}) \sqrt{12}$

Step 1.1.2

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

$(6 \sqrt{2^{2} \cdot 3} - \sqrt{12}) \sqrt{12}$

Step 1.2

Pull terms out from under the radical.

$(6 (2 \sqrt{3}) - \sqrt{12}) \sqrt{12}$

Step 1.3

Multiply $2$ by $6$ .

$(12 \sqrt{3} - \sqrt{12}) \sqrt{12}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $12$ .

$(12 \sqrt{3} - \sqrt{4 (3)}) \sqrt{12}$

Step 1.4.2

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

$(12 \sqrt{3} - \sqrt{2^{2} \cdot 3}) \sqrt{12}$

Step 1.5

Pull terms out from under the radical.

$(12 \sqrt{3} - (2 \sqrt{3})) \sqrt{12}$

Step 1.6

Multiply $2$ by $- 1$ .

$(12 \sqrt{3} - 2 \sqrt{3}) \sqrt{12}$

Step 2

Subtract $2 \sqrt{3}$ from $12 \sqrt{3}$ .

$10 \sqrt{3} \sqrt{12}$

Step 3

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

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Step 3.1

Factor $4$ out of $12$ .

$10 \sqrt{3} \sqrt{4 (3)}$

Step 3.2

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

$10 \sqrt{3} \sqrt{2^{2} \cdot 3}$

Step 4

Pull terms out from under the radical.

$10 \sqrt{3} (2 \sqrt{3})$

Step 5

Multiply $10 \sqrt{3} (2 \sqrt{3})$ .

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Step 5.1

Multiply $2$ by $10$ .

$20 \sqrt{3} \sqrt{3}$

Step 5.2

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

$20 ({\sqrt{3}}^{1} \sqrt{3})$

Step 5.3

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

$20 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Step 5.4

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

$20 {\sqrt{3}}^{1 + 1}$

Step 5.5

Add $1$ and $1$ .

$20 {\sqrt{3}}^{2}$

Step 6

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

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Step 6.1

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

$20 {(3^{\frac{1}{2}})}^{2}$

Step 6.2

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

$20 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 6.3

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

$20 \cdot 3^{\frac{2}{2}}$

Step 6.4

Cancel the common factor of $2$ .

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Step 6.4.1

Cancel the common factor.

$20 \cdot 3^{\frac{2}{2}}$

Step 6.4.2

Rewrite the expression.

$20 \cdot 3^{1}$

Step 6.5

Evaluate the exponent.

$20 \cdot 3$

Step 7

Multiply $20$ by $3$ .

$60$