Solve the Rational Equation for v 6 = square root of v-2

$6 = \sqrt{v - 2}$

Rewrite the equation as $\sqrt{v - 2} = 6$ .

$\sqrt{v - 2} = 6$

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

${\sqrt{v - 2}}^{2} = 6^{2}$

Simplify each side of the equation.

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

${({(v - 2)}^{\frac{1}{2}})}^{2} = 6^{2}$

Simplify the left side.

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

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

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

${(v - 2)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(v - 2)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

${(v - 2)}^{1} = 6^{2}$

Simplify.

$v - 2 = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$v - 2 = 36$

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

Add $2$ to both sides of the equation.

$v = 36 + 2$

Add $36$ and $2$ .

$v = 38$