Pre-Algebra Examples

${(\sqrt{24} \div 2)}^{2}$

Step 1

Rewrite the division as a fraction.

${(\frac{\sqrt{24}}{2})}^{2}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $24$ as $2^{2} \cdot 6$ .

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Step 2.1.1

Factor $4$ out of $24$ .

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

Step 2.1.2

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

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

Step 2.2

Pull terms out from under the radical.

${(\frac{2 \sqrt{6}}{2})}^{2}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Cancel the common factor.

${(\frac{2 \sqrt{6}}{2})}^{2}$

Step 3.1.2

Divide $\sqrt{6}$ by $1$ .

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

Step 3.2

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

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Step 3.2.1

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

${(6^{\frac{1}{2}})}^{2}$

Step 3.2.2

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

$6^{\frac{1}{2} \cdot 2}$

Step 3.2.3

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

$6^{\frac{2}{2}}$

Step 3.2.4

Cancel the common factor of $2$ .

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Step 3.2.4.1

Cancel the common factor.

$6^{\frac{2}{2}}$

Step 3.2.4.2

Rewrite the expression.

$6^{1}$

Step 3.2.5

Evaluate the exponent.

$6$