Finite Math Examples

${(\sqrt{12} + 5 \sqrt{3})}^{2}$

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 $12$ .

${(\sqrt{4 (3)} + 5 \sqrt{3})}^{2}$

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

${(2 \sqrt{3} + 5 \sqrt{3})}^{2}$

Step 2

Simplify terms.

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Step 2.1

Add $2 \sqrt{3}$ and $5 \sqrt{3}$ .

${(7 \sqrt{3})}^{2}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Apply the product rule to $7 \sqrt{3}$ .

$7^{2} {\sqrt{3}}^{2}$

Step 2.2.2

Raise $7$ to the power of $2$ .

$49 {\sqrt{3}}^{2}$

Step 2.3

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

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Step 2.3.1

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

$49 {(3^{\frac{1}{2}})}^{2}$

Step 2.3.2

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

$49 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 2.3.3

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

$49 \cdot 3^{\frac{2}{2}}$

Step 2.3.4

Cancel the common factor of $2$ .

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Step 2.3.4.1

Cancel the common factor.

$49 \cdot 3^{\frac{2}{2}}$

Step 2.3.4.2

Rewrite the expression.

$49 \cdot 3^{1}$

Step 2.3.5

Evaluate the exponent.

$49 \cdot 3$

Step 2.4

Multiply $49$ by $3$ .

$147$