Solve for v square root of v-12-5=2

$\sqrt{v - 12 - 5} = 2$

Step 1

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

${\sqrt{v - 12 - 5}}^{2} = 2^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{v - 12 - 5}$ as ${(v - 12 - 5)}^{\frac{1}{2}}$ .

${({(v - 12 - 5)}^{\frac{1}{2}})}^{2} = 2^{2}$

Simplify the left side.

Simplify ${({(v - 12 - 5)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(v - 12 - 5)}^{\frac{1}{2}})}^{2}$ .

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

${(v - 12 - 5)}^{\frac{1}{2} \cdot 2} = 2^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(v - 12 - 5)}^{\frac{1}{2} \cdot 2} = 2^{2}$

Rewrite the expression.

${(v - 12 - 5)}^{1} = 2^{2}$

Subtract $5$ from $- 12$ .

${(v - 17)}^{1} = 2^{2}$

Simplify.

$v - 17 = 2^{2}$

Simplify the right side.

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

$v - 17 = 4$

Step 3

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

Add $17$ to both sides of the equation.

$v = 4 + 17$

Add $4$ and $17$ .

$v = 21$