Solve for x 9 = square root of x/3+1

$9 = \sqrt{\frac{x}{3}} + 1$

Step 1

Rewrite the equation as $\sqrt{\frac{x}{3}} + 1 = 9$ .

$\sqrt{\frac{x}{3}} + 1 = 9$

Step 2

Move all terms not containing $\sqrt{\frac{x}{3}}$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$\sqrt{\frac{x}{3}} = 9 - 1$

Subtract $1$ from $9$ .

$\sqrt{\frac{x}{3}} = 8$

Step 3

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

${\sqrt{\frac{x}{3}}}^{2} = 8^{2}$

Step 4

Simplify each side of the equation.

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

${({(\frac{x}{3})}^{\frac{1}{2}})}^{2} = 8^{2}$

Simplify the left side.

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

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

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

${(\frac{x}{3})}^{\frac{1}{2} \cdot 2} = 8^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{x}{3})}^{\frac{1}{2} \cdot 2} = 8^{2}$

Rewrite the expression.

${(\frac{x}{3})}^{1} = 8^{2}$

Simplify.

$\frac{x}{3} = 8^{2}$

Simplify the right side.

Raise $8$ to the power of $2$ .

$\frac{x}{3} = 64$

Step 5

Solve for $x$ .

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 \cdot 64$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x}{3} = 3 \cdot 64$

Rewrite the expression.

$x = 3 \cdot 64$

Simplify the right side.

Multiply $3$ by $64$ .

$x = 192$

Solve for x 9 = square root of x/3+1

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