Solve for q square root of 3q=6

$\sqrt{3 q} = 6$

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

${\sqrt{3 q}}^{2} = 6^{2}$

Simplify each side of the equation.

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

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

Simplify the left side.

Simplify ${({(3 q)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 q)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

${(3 q)}^{1} = 6^{2}$

Simplify.

$3 q = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$3 q = 36$

Divide each term in $3 q = 36$ by $3$ and simplify.

Divide each term in $3 q = 36$ by $3$ .

$\frac{3 q}{3} = \frac{36}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 q}{3} = \frac{36}{3}$

Divide $q$ by $1$ .

$q = \frac{36}{3}$

Simplify the right side.

Divide $36$ by $3$ .

$q = 12$