Pre-Algebra Examples

$\sqrt{\frac{x}{10}} = \sqrt{3 x - 58}$

Step 1

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

${\sqrt{\frac{x}{10}}}^{2} = {\sqrt{3 x - 58}}^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{x}{10}}$ as ${(\frac{x}{10})}^{\frac{1}{2}}$ .

${({(\frac{x}{10})}^{\frac{1}{2}})}^{2} = {\sqrt{3 x - 58}}^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(\frac{x}{10})}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(\frac{x}{10})}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(\frac{x}{10})}^{\frac{1}{2} \cdot 2} = {\sqrt{3 x - 58}}^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(\frac{x}{10})}^{\frac{1}{2} \cdot 2} = {\sqrt{3 x - 58}}^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(\frac{x}{10})}^{1} = {\sqrt{3 x - 58}}^{2}$

Step 2.2.1.2

Simplify.

$\frac{x}{10} = {\sqrt{3 x - 58}}^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Rewrite ${\sqrt{3 x - 58}}^{2}$ as $3 x - 58$ .

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Step 2.3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 58}$ as ${(3 x - 58)}^{\frac{1}{2}}$ .

$\frac{x}{10} = {({(3 x - 58)}^{\frac{1}{2}})}^{2}$

Step 2.3.1.2

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

$\frac{x}{10} = {(3 x - 58)}^{\frac{1}{2} \cdot 2}$

Step 2.3.1.3

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

$\frac{x}{10} = {(3 x - 58)}^{\frac{2}{2}}$

Step 2.3.1.4

Cancel the common factor of $2$ .

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Step 2.3.1.4.1

Cancel the common factor.

$\frac{x}{10} = {(3 x - 58)}^{\frac{2}{2}}$

Step 2.3.1.4.2

Rewrite the expression.

$\frac{x}{10} = {(3 x - 58)}^{1}$

Step 2.3.1.5

Simplify.

$\frac{x}{10} = 3 x - 58$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $10$ .

$\frac{x}{10} \cdot 10 = (3 x - 58) \cdot 10$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Cancel the common factor of $10$ .

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Step 3.2.1.1.1

Cancel the common factor.

$\frac{x}{10} \cdot 10 = (3 x - 58) \cdot 10$

Step 3.2.1.1.2

Rewrite the expression.

$x = (3 x - 58) \cdot 10$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(3 x - 58) \cdot 10$ .

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Step 3.2.2.1.1

Apply the distributive property.

$x = 3 x \cdot 10 - 58 \cdot 10$

Step 3.2.2.1.2

Multiply.

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Step 3.2.2.1.2.1

Multiply $10$ by $3$ .

$x = 30 x - 58 \cdot 10$

Step 3.2.2.1.2.2

Multiply $- 58$ by $10$ .

$x = 30 x - 580$

Step 3.3

Solve for $x$ .

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Step 3.3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.3.1.1

Subtract $30 x$ from both sides of the equation.

$x - 30 x = - 580$

Step 3.3.1.2

Subtract $30 x$ from $x$ .

$- 29 x = - 580$

Step 3.3.2

Divide each term in $- 29 x = - 580$ by $- 29$ and simplify.

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Step 3.3.2.1

Divide each term in $- 29 x = - 580$ by $- 29$ .

$\frac{- 29 x}{- 29} = \frac{- 580}{- 29}$

Step 3.3.2.2

Simplify the left side.

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Step 3.3.2.2.1

Cancel the common factor of $- 29$ .

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Step 3.3.2.2.1.1

Cancel the common factor.

$\frac{- 29 x}{- 29} = \frac{- 580}{- 29}$

Step 3.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 580}{- 29}$

Step 3.3.2.3

Simplify the right side.

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Step 3.3.2.3.1

Divide $- 580$ by $- 29$ .

$x = 20$