Solve for v square root of v-4=3

$\sqrt{v - 4} = 3$

Step 1

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

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

Step 2

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$v - 4 = 3^{2}$

Simplify the right side.

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

$v - 4 = 9$

Step 3

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

Add $4$ to both sides of the equation.

$v = 9 + 4$

Add $9$ and $4$ .

$v = 13$