Solve by Factoring square root of r+5=11

$\sqrt{r + 5} = 11$

Step 1

Subtract $11$ from both sides of the equation.

$\sqrt{r + 5} - 11 = 0$

Step 2

Add $11$ to both sides of the equation.

$\sqrt{r + 5} = 11$

Step 3

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

${\sqrt{r + 5}}^{2} = 11^{2}$

Step 4

Simplify each side of the equation.

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

${({(r + 5)}^{\frac{1}{2}})}^{2} = 11^{2}$

Simplify the left side.

Simplify ${({(r + 5)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(r + 5)}^{\frac{1}{2}})}^{2}$ .

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

${(r + 5)}^{\frac{1}{2} \cdot 2} = 11^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(r + 5)}^{\frac{1}{2} \cdot 2} = 11^{2}$

Rewrite the expression.

${(r + 5)}^{1} = 11^{2}$

Simplify.

$r + 5 = 11^{2}$

Simplify the right side.

Raise $11$ to the power of $2$ .

$r + 5 = 121$

Step 5

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

Subtract $5$ from both sides of the equation.

$r = 121 - 5$

Subtract $5$ from $121$ .

$r = 116$