Solve for q square root of 9q-8=8

$\sqrt{9 q - 8} = 8$

Step 1

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

${\sqrt{9 q - 8}}^{2} = 8^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{9 q - 8}$ as ${(9 q - 8)}^{\frac{1}{2}}$ .

${({(9 q - 8)}^{\frac{1}{2}})}^{2} = 8^{2}$

Simplify the left side.

Simplify ${({(9 q - 8)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(9 q - 8)}^{\frac{1}{2}})}^{2}$ .

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

${(9 q - 8)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(9 q - 8)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Rewrite the expression.

${(9 q - 8)}^{1} = 8^{2}$

Simplify.

$9 q - 8 = 8^{2}$

Simplify the right side.

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

$9 q - 8 = 64$

Step 3

Solve for $q$ .

Move all terms not containing $q$ to the right side of the equation.

Add $8$ to both sides of the equation.

$9 q = 64 + 8$

Add $64$ and $8$ .

$9 q = 72$

Divide each term in $9 q = 72$ by $9$ and simplify.

Divide each term in $9 q = 72$ by $9$ .

$\frac{9 q}{9} = \frac{72}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 q}{9} = \frac{72}{9}$

Divide $q$ by $1$ .

$q = \frac{72}{9}$

Simplify the right side.

Divide $72$ by $9$ .

$q = 8$