Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

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

Step 2.4.2

Rewrite the expression.

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

Step 2.5

Evaluate the exponent.

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

Step 3

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

$\frac{6}{4}$

Step 4

Cancel the common factor of $6$ and $4$ .

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Step 4.1

Factor $2$ out of $6$ .

$\frac{2 (3)}{4}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $4$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$\frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$