Solve for x square root of (2x)/3=6

$\sqrt{\frac{2 x}{3}} = 6$

Step 1

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

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

Step 2

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

$\frac{2 x}{3} = 36$

Step 3

Solve for $x$ .

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot 36$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 x}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot 36$

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot 36$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{3}{2} \cdot 36$

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot 36$

Rewrite the expression.

$x = \frac{3}{2} \cdot 36$

Simplify the right side.

Simplify $\frac{3}{2} \cdot 36$ .

Cancel the common factor of $2$ .

Factor $2$ out of $36$ .

$x = \frac{3}{2} \cdot (2 (18))$

Cancel the common factor.

$x = \frac{3}{2} \cdot (2 \cdot 18)$

Rewrite the expression.

$x = 3 \cdot 18$

Multiply $3$ by $18$ .

$x = 54$

Solve for x square root of (2x)/3=6

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