Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $2 \sqrt{3}$ .

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

Step 1.2

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

$4 {\sqrt{3}}^{2} + {(2 \sqrt{6})}^{2}$

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

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

$4 \cdot 3^{\frac{1}{2} \cdot 2} + {(2 \sqrt{6})}^{2}$

Step 1.3.3

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

$4 \cdot 3^{\frac{2}{2}} + {(2 \sqrt{6})}^{2}$

Step 1.3.4

Cancel the common factor of $2$ .

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Step 1.3.4.1

Cancel the common factor.

$4 \cdot 3^{\frac{2}{2}} + {(2 \sqrt{6})}^{2}$

Step 1.3.4.2

Rewrite the expression.

$4 \cdot 3^{1} + {(2 \sqrt{6})}^{2}$

Step 1.3.5

Evaluate the exponent.

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

Step 1.4

Multiply $4$ by $3$ .

$12 + {(2 \sqrt{6})}^{2}$

Step 1.5

Apply the product rule to $2 \sqrt{6}$ .

$12 + 2^{2} {\sqrt{6}}^{2}$

Step 1.6

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

$12 + 4 {\sqrt{6}}^{2}$

Step 1.7

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

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Step 1.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$12 + 4 {(6^{\frac{1}{2}})}^{2}$

Step 1.7.2

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

$12 + 4 \cdot 6^{\frac{1}{2} \cdot 2}$

Step 1.7.3

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

$12 + 4 \cdot 6^{\frac{2}{2}}$

Step 1.7.4

Cancel the common factor of $2$ .

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Step 1.7.4.1

Cancel the common factor.

$12 + 4 \cdot 6^{\frac{2}{2}}$

Step 1.7.4.2

Rewrite the expression.

$12 + 4 \cdot 6^{1}$

Step 1.7.5

Evaluate the exponent.

$12 + 4 \cdot 6$

Step 1.8

Multiply $4$ by $6$ .

$12 + 24$

Step 2

Add $12$ and $24$ .

$36$