Solve for x square root of 2x-88 = square root of x/6

$\sqrt{2 x - 88} = \sqrt{\frac{x}{6}}$

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

${\sqrt{2 x - 88}}^{2} = {\sqrt{\frac{x}{6}}}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x - 88}$ as ${(2 x - 88)}^{\frac{1}{2}}$ .

${({(2 x - 88)}^{\frac{1}{2}})}^{2} = {\sqrt{\frac{x}{6}}}^{2}$

Simplify the left side.

Simplify ${({(2 x - 88)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 x - 88)}^{\frac{1}{2}})}^{2}$ .

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

${(2 x - 88)}^{\frac{1}{2} \cdot 2} = {\sqrt{\frac{x}{6}}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x - 88)}^{\frac{1}{2} \cdot 2} = {\sqrt{\frac{x}{6}}}^{2}$

Rewrite the expression.

${(2 x - 88)}^{1} = {\sqrt{\frac{x}{6}}}^{2}$

Simplify.

$2 x - 88 = {\sqrt{\frac{x}{6}}}^{2}$

Simplify the right side.

Simplify ${\sqrt{\frac{x}{6}}}^{2}$ .

Rewrite $\sqrt{\frac{x}{6}}$ as $\frac{\sqrt{x}}{\sqrt{6}}$ .

$2 x - 88 = {(\frac{\sqrt{x}}{\sqrt{6}})}^{2}$

Multiply $\frac{\sqrt{x}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$2 x - 88 = {(\frac{\sqrt{x}}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}})}^{2}$

Simplify terms.

Combine and simplify the denominator.

Multiply $\frac{\sqrt{x}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$2 x - 88 = {(\frac{\sqrt{x} \sqrt{6}}{\sqrt{6} \sqrt{6}})}^{2}$

Raise $\sqrt{6}$ to the power of $1$ .

$2 x - 88 = {(\frac{\sqrt{x} \sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}})}^{2}$

Raise $\sqrt{6}$ to the power of $1$ .

$2 x - 88 = {(\frac{\sqrt{x} \sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}})}^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 x - 88 = {(\frac{\sqrt{x} \sqrt{6}}{{\sqrt{6}}^{1 + 1}})}^{2}$

Add $1$ and $1$ .

$2 x - 88 = {(\frac{\sqrt{x} \sqrt{6}}{{\sqrt{6}}^{2}})}^{2}$

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

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

$2 x - 88 = {(\frac{\sqrt{x} \sqrt{6}}{{(6^{\frac{1}{2}})}^{2}})}^{2}$

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

$2 x - 88 = {(\frac{\sqrt{x} \sqrt{6}}{6^{\frac{1}{2} \cdot 2}})}^{2}$

Combine $\frac{1}{2}$ and $2$ .

$2 x - 88 = {(\frac{\sqrt{x} \sqrt{6}}{6^{\frac{2}{2}}})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 x - 88 = {(\frac{\sqrt{x} \sqrt{6}}{6^{\frac{2}{2}}})}^{2}$

Rewrite the expression.

$2 x - 88 = {(\frac{\sqrt{x} \sqrt{6}}{6^{1}})}^{2}$

Evaluate the exponent.

$2 x - 88 = {(\frac{\sqrt{x} \sqrt{6}}{6})}^{2}$

Combine using the product rule for radicals.

$2 x - 88 = {(\frac{\sqrt{x \cdot 6}}{6})}^{2}$

Apply the product rule to $\frac{\sqrt{x \cdot 6}}{6}$ .

$2 x - 88 = \frac{{\sqrt{x \cdot 6}}^{2}}{6^{2}}$

Simplify the numerator.

Rewrite ${\sqrt{x \cdot 6}}^{2}$ as $x \cdot 6$ .

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

$2 x - 88 = \frac{{({(x \cdot 6)}^{\frac{1}{2}})}^{2}}{6^{2}}$

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

$2 x - 88 = \frac{{(x \cdot 6)}^{\frac{1}{2} \cdot 2}}{6^{2}}$

Combine $\frac{1}{2}$ and $2$ .

$2 x - 88 = \frac{{(x \cdot 6)}^{\frac{2}{2}}}{6^{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 x - 88 = \frac{{(x \cdot 6)}^{\frac{2}{2}}}{6^{2}}$

Rewrite the expression.

$2 x - 88 = \frac{{(x \cdot 6)}^{1}}{6^{2}}$

Simplify.

$2 x - 88 = \frac{x \cdot 6}{6^{2}}$

Move $6$ to the left of $x$ .

$2 x - 88 = \frac{6 x}{6^{2}}$

Reduce the expression by cancelling the common factors.

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

$2 x - 88 = \frac{6 x}{36}$

Cancel the common factor of $6$ and $36$ .

Factor $6$ out of $6 x$ .

$2 x - 88 = \frac{6 (x)}{36}$

Cancel the common factors.

Factor $6$ out of $36$ .

$2 x - 88 = \frac{6 x}{6 \cdot 6}$

Cancel the common factor.

$2 x - 88 = \frac{6 x}{6 \cdot 6}$

Rewrite the expression.

$2 x - 88 = \frac{x}{6}$

Solve for $x$ .

Multiply both sides by $6$ .

$(2 x - 88) \cdot 6 = \frac{x}{6} \cdot 6$

Simplify.

Simplify the left side.

Simplify $(2 x - 88) \cdot 6$ .

Apply the distributive property.

$2 x \cdot 6 - 88 \cdot 6 = \frac{x}{6} \cdot 6$

Multiply.

Multiply $6$ by $2$ .

$12 x - 88 \cdot 6 = \frac{x}{6} \cdot 6$

Multiply $- 88$ by $6$ .

$12 x - 528 = \frac{x}{6} \cdot 6$

Simplify the right side.

Cancel the common factor of $6$ .

Cancel the common factor.

$12 x - 528 = \frac{x}{6} \cdot 6$

Rewrite the expression.

$12 x - 528 = x$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$12 x - 528 - x = 0$

Subtract $x$ from $12 x$ .

$11 x - 528 = 0$

Add $528$ to both sides of the equation.

$11 x = 528$

Divide each term in $11 x = 528$ by $11$ and simplify.

Divide each term in $11 x = 528$ by $11$ .

$\frac{11 x}{11} = \frac{528}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{528}{11}$

Divide $x$ by $1$ .

$x = \frac{528}{11}$

Simplify the right side.

Divide $528$ by $11$ .

$x = 48$

Solve for x square root of 2x-88 = square root of x/6

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