Solve the Rational Equation for v square root of v+3-1=7

$\sqrt{v + 3} - 1 = 7$

Step 1

Move all terms not containing $\sqrt{v + 3}$ to the right side of the equation.

Add $1$ to both sides of the equation.

$\sqrt{v + 3} = 7 + 1$

Add $7$ and $1$ .

$\sqrt{v + 3} = 8$

Step 2

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

${\sqrt{v + 3}}^{2} = 8^{2}$

Step 3

Simplify each side of the equation.

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

${({(v + 3)}^{\frac{1}{2}})}^{2} = 8^{2}$

Simplify the left side.

Simplify ${({(v + 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(v + 3)}^{\frac{1}{2}})}^{2}$ .

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

${(v + 3)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(v + 3)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Rewrite the expression.

${(v + 3)}^{1} = 8^{2}$

Simplify.

$v + 3 = 8^{2}$

Simplify the right side.

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

$v + 3 = 64$

Step 4

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

Subtract $3$ from both sides of the equation.

$v = 64 - 3$

Subtract $3$ from $64$ .

$v = 61$