Solve for z square root of z+13=3

$\sqrt{z + 13} = 3$

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

${\sqrt{z + 13}}^{2} = 3^{2}$

Simplify each side of the equation.

Tap for more steps…

Multiply the exponents in ${({(z + 13)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps…

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

${(z + 13)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Tap for more steps…

Cancel the common factor.

${(z + 13)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(z + 13)}^{1} = 3^{2}$

Simplify.

$z + 13 = 3^{2}$

Raise $3$ to the power of $2$ .

$z + 13 = 9$

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

Tap for more steps…

Subtract $13$ from both sides of the equation.

$z = 9 - 13$

Subtract $13$ from $9$ .

$z = - 4$

Solve for z square root of z+13=3