Algebra Examples

$y = \sqrt{\frac{x - 48}{6}}$

Step 1

Rewrite the equation as $\sqrt{\frac{x - 48}{6}} = y$ .

$\sqrt{\frac{x - 48}{6}} = y$

Step 2

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

${\sqrt{\frac{x - 48}{6}}}^{2} = y^{2}$

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 $\sqrt{\frac{x - 48}{6}}$ as ${(\frac{x - 48}{6})}^{\frac{1}{2}}$ .

${({(\frac{x - 48}{6})}^{\frac{1}{2}})}^{2} = y^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(\frac{x - 48}{6})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(\frac{x - 48}{6})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(\frac{x - 48}{6})}^{\frac{1}{2} \cdot 2} = y^{2}$

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.

${(\frac{x - 48}{6})}^{\frac{1}{2} \cdot 2} = y^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(\frac{x - 48}{6})}^{1} = y^{2}$

Step 3.2.1.2

Simplify.

$\frac{x - 48}{6} = y^{2}$

Step 4

Solve for $x$ .

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Step 4.1

Multiply both sides of the equation by $6$ .

$6 \frac{x - 48}{6} = 6 y^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$6 \frac{x - 48}{6} = 6 y^{2}$

Step 4.2.1.2

Rewrite the expression.

$x - 48 = 6 y^{2}$

Step 4.3

Add $48$ to both sides of the equation.

$x = 6 y^{2} + 48$