Pre-Algebra Examples

$5 \sqrt{12} \cdot (6 \sqrt{3})$

Step 1

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

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Step 1.1

Factor $4$ out of $12$ .

$5 \sqrt{4 (3)} \cdot (6 \sqrt{3})$

Step 1.2

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

$5 \sqrt{2^{2} \cdot 3} \cdot (6 \sqrt{3})$

Step 2

Pull terms out from under the radical.

$5 (2 \sqrt{3}) \cdot (6 \sqrt{3})$

Step 3

Multiply $2$ by $5$ .

$10 \sqrt{3} \cdot (6 \sqrt{3})$

Step 4

Multiply $10 \sqrt{3} (6 \sqrt{3})$ .

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Step 4.1

Multiply $6$ by $10$ .

$60 \sqrt{3} \sqrt{3}$

Step 4.2

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

$60 ({\sqrt{3}}^{1} \sqrt{3})$

Step 4.3

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

$60 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Step 4.4

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

$60 {\sqrt{3}}^{1 + 1}$

Step 4.5

Add $1$ and $1$ .

$60 {\sqrt{3}}^{2}$

Step 5

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

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Step 5.1

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

$60 {(3^{\frac{1}{2}})}^{2}$

Step 5.2

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

$60 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 5.3

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

$60 \cdot 3^{\frac{2}{2}}$

Step 5.4

Cancel the common factor of $2$ .

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Step 5.4.1

Cancel the common factor.

$60 \cdot 3^{\frac{2}{2}}$

Step 5.4.2

Rewrite the expression.

$60 \cdot 3^{1}$

Step 5.5

Evaluate the exponent.

$60 \cdot 3$

Step 6

Multiply $60$ by $3$ .

$180$