Basic Math Examples

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

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 $12$ .

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

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 2

Simplify terms.

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.2.4

Cancel the common factor of $2$ .

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Step 2.2.4.1

Cancel the common factor.

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

Step 2.2.4.2

Rewrite the expression.

$3^{1}$

Step 2.2.5

Evaluate the exponent.

$3$