Solve for q square root of 4q-3=3

$\sqrt{4 q - 3} = 3$

Step 1

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

${\sqrt{4 q - 3}}^{2} = 3^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 q - 3}$ as ${(4 q - 3)}^{\frac{1}{2}}$ .

${({(4 q - 3)}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

Simplify ${({(4 q - 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 q - 3)}^{\frac{1}{2}})}^{2}$ .

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

${(4 q - 3)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 q - 3)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(4 q - 3)}^{1} = 3^{2}$

Simplify.

$4 q - 3 = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$4 q - 3 = 9$

Step 3

Solve for $q$ .

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

Add $3$ to both sides of the equation.

$4 q = 9 + 3$

Add $9$ and $3$ .

$4 q = 12$

Divide each term in $4 q = 12$ by $4$ and simplify.

Divide each term in $4 q = 12$ by $4$ .

$\frac{4 q}{4} = \frac{12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 q}{4} = \frac{12}{4}$

Divide $q$ by $1$ .

$q = \frac{12}{4}$

Simplify the right side.

Divide $12$ by $4$ .

$q = 3$