Algebra Examples

$\frac{12.7}{2.76} = \sqrt{\frac{x}{32}}$

Step 1

Rewrite the equation as $\sqrt{\frac{x}{32}} = \frac{12.7}{2.76}$ .

$\sqrt{\frac{x}{32}} = \frac{12.7}{2.76}$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{\frac{x}{32}}}^{2} = {(\frac{12.7}{2.76})}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{x}{32}}$ as ${(\frac{x}{32})}^{\frac{1}{2}}$ .

${({(\frac{x}{32})}^{\frac{1}{2}})}^{2} = {(\frac{12.7}{2.76})}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(\frac{x}{32})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(\frac{x}{32})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(\frac{x}{32})}^{\frac{1}{2} \cdot 2} = {(\frac{12.7}{2.76})}^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(\frac{x}{32})}^{\frac{1}{2} \cdot 2} = {(\frac{12.7}{2.76})}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(\frac{x}{32})}^{1} = {(\frac{12.7}{2.76})}^{2}$

Step 3.2.1.2

Multiply by $1$ .

${(\frac{1 x}{32})}^{1} = {(\frac{12.7}{2.76})}^{2}$

Step 3.2.1.3

Factor $32$ out of $32$ .

${(\frac{1 x}{32 (1)})}^{1} = {(\frac{12.7}{2.76})}^{2}$

Step 3.2.1.4

Separate fractions.

${(\frac{1}{32} \cdot \frac{x}{1})}^{1} = {(\frac{12.7}{2.76})}^{2}$

Step 3.2.1.5

Divide $1$ by $32$ .

${(0.03125 \frac{x}{1})}^{1} = {(\frac{12.7}{2.76})}^{2}$

Step 3.2.1.6

Cancel the common factor of $0.03125$ .

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Step 3.2.1.6.1

Factor $0.03125$ out of $1$ .

${(0.03125 \frac{x}{0.03125 \cdot 32})}^{1} = {(\frac{12.7}{2.76})}^{2}$

Step 3.2.1.6.2

Cancel the common factor.

${(0.03125 \frac{x}{0.03125 \cdot 32})}^{1} = {(\frac{12.7}{2.76})}^{2}$

Step 3.2.1.6.3

Rewrite the expression.

${(\frac{x}{32})}^{1} = {(\frac{12.7}{2.76})}^{2}$

Step 3.2.1.7

Simplify.

$\frac{x}{32} = {(\frac{12.7}{2.76})}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(\frac{12.7}{2.76})}^{2}$ .

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Step 3.3.1.1

Divide $12.7$ by $2.76$ .

$\frac{x}{32} = {4.60144927}^{2}$

Step 3.3.1.2

Raise $4.60144927$ to the power of $2$ .

$\frac{x}{32} = 21.17333543$

Step 4

Solve for $x$ .

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Step 4.1

Multiply both sides of the equation by $32$ .

$32 \frac{x}{32} = 32 \cdot 21.17333543$

Step 4.2

Simplify both sides of the equation.

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Cancel the common factor of $32$ .

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Step 4.2.1.1.1

Cancel the common factor.

$32 \frac{x}{32} = 32 \cdot 21.17333543$

Step 4.2.1.1.2

Rewrite the expression.

$x = 32 \cdot 21.17333543$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Multiply $32$ by $21.17333543$ .

$x = 677.54673387$