Solve the Rational Equation for x 3 = square root of x/5

$3 = \sqrt{\frac{x}{5}}$

Step 1

Rewrite the equation as $\sqrt{\frac{x}{5}} = 3$ .

$\sqrt{\frac{x}{5}} = 3$

Step 2

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

${\sqrt{\frac{x}{5}}}^{2} = 3^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{x}{5}}$ as ${(\frac{x}{5})}^{\frac{1}{2}}$ .

${({(\frac{x}{5})}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

Simplify ${({(\frac{x}{5})}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(\frac{x}{5})}^{\frac{1}{2}})}^{2}$ .

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

${(\frac{x}{5})}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{x}{5})}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(\frac{x}{5})}^{1} = 3^{2}$

Simplify.

$\frac{x}{5} = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$\frac{x}{5} = 9$

Step 4

Solve for $x$ .

Multiply both sides of the equation by $5$ .

$5 \frac{x}{5} = 5 \cdot 9$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{x}{5} = 5 \cdot 9$

Rewrite the expression.

$x = 5 \cdot 9$

Simplify the right side.

Multiply $5$ by $9$ .

$x = 45$