Evaluate 10 = square root of 14r+2

$10 = \sqrt{14 r + 2}$

Rewrite the equation as $\sqrt{14 r + 2} = 10$ .

$\sqrt{14 r + 2} = 10$

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

${\sqrt{14 r + 2}}^{2} = 10^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{14 r + 2}$ as ${(14 r + 2)}^{\frac{1}{2}}$ .

${({(14 r + 2)}^{\frac{1}{2}})}^{2} = 10^{2}$

Simplify the left side.

Simplify ${({(14 r + 2)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(14 r + 2)}^{\frac{1}{2}})}^{2}$ .

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

${(14 r + 2)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(14 r + 2)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Rewrite the expression.

${(14 r + 2)}^{1} = 10^{2}$

Simplify.

$14 r + 2 = 10^{2}$

Simplify the right side.

Raise $10$ to the power of $2$ .

$14 r + 2 = 100$

Solve for $r$ .

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

Subtract $2$ from both sides of the equation.

$14 r = 100 - 2$

Subtract $2$ from $100$ .

$14 r = 98$

Divide each term in $14 r = 98$ by $14$ and simplify.

Divide each term in $14 r = 98$ by $14$ .

$\frac{14 r}{14} = \frac{98}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 r}{14} = \frac{98}{14}$

Divide $r$ by $1$ .

$r = \frac{98}{14}$

Simplify the right side.

Divide $98$ by $14$ .

$r = 7$