Solve the Rational Equation for k -6+ square root of k/6=-3

$- 6 + \sqrt{\frac{k}{6}} = - 3$

Move all terms not containing $\sqrt{\frac{k}{6}}$ to the right side of the equation.

Add $6$ to both sides of the equation.

$\sqrt{\frac{k}{6}} = - 3 + 6$

Add $- 3$ and $6$ .

$\sqrt{\frac{k}{6}} = 3$

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

${\sqrt{\frac{k}{6}}}^{2} = 3^{2}$

Simplify each side of the equation.

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

${({(\frac{k}{6})}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

Simplify ${({(\frac{k}{6})}^{\frac{1}{2}})}^{2}$ .

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

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

${(\frac{k}{6})}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{k}{6})}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(\frac{k}{6})}^{1} = 3^{2}$

Simplify.

$\frac{k}{6} = 3^{2}$

Simplify the right side.

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

$\frac{k}{6} = 9$

Solve for $k$ .

Multiply both sides of the equation by $6$ .

$6 \frac{k}{6} = 6 \cdot 9$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$6 \frac{k}{6} = 6 \cdot 9$

Rewrite the expression.

$k = 6 \cdot 9$

Simplify the right side.

Multiply $6$ by $9$ .

$k = 54$