Pre-Algebra Examples

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

Step 1

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

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Step 1.1

Factor $4$ out of $12$ .

$\sqrt{4 (3)} (6 \sqrt{2} - \sqrt{12})$

Step 1.2

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Factor $4$ out of $12$ .

$2 \sqrt{3} (6 \sqrt{2} - \sqrt{4 (3)})$

Step 3.1.2

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

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

Step 3.2

Pull terms out from under the radical.

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

Step 3.3

Multiply $2$ by $- 1$ .

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $2 \sqrt{3} (6 \sqrt{2})$ .

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Step 5.1

Multiply $6$ by $2$ .

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

Step 5.2

Combine using the product rule for radicals.

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

Step 5.3

Multiply $2$ by $3$ .

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

Step 6

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

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Step 6.1

Multiply $- 2$ by $2$ .

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

Step 6.2

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

$12 \sqrt{6} - 4 ({\sqrt{3}}^{1} \sqrt{3})$

Step 6.3

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

$12 \sqrt{6} - 4 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Step 6.4

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

$12 \sqrt{6} - 4 {\sqrt{3}}^{1 + 1}$

Step 6.5

Add $1$ and $1$ .

$12 \sqrt{6} - 4 {\sqrt{3}}^{2}$

Step 7

Simplify each term.

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Step 7.1

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

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Step 7.1.1

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

$12 \sqrt{6} - 4 {(3^{\frac{1}{2}})}^{2}$

Step 7.1.2

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

$12 \sqrt{6} - 4 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 7.1.3

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

$12 \sqrt{6} - 4 \cdot 3^{\frac{2}{2}}$

Step 7.1.4

Cancel the common factor of $2$ .

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Step 7.1.4.1

Cancel the common factor.

$12 \sqrt{6} - 4 \cdot 3^{\frac{2}{2}}$

Step 7.1.4.2

Rewrite the expression.

$12 \sqrt{6} - 4 \cdot 3^{1}$

Step 7.1.5

Evaluate the exponent.

$12 \sqrt{6} - 4 \cdot 3$

Step 7.2

Multiply $- 4$ by $3$ .

$12 \sqrt{6} - 12$

Step 8

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{6} - 12$

Decimal Form:

$17.39387691 \dots$