Solve for z square root of z+9=0

$\sqrt{z} + 9 = 0$

Subtract $9$ from both sides of the equation.

$\sqrt{z} = - 9$

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

${\sqrt{z}}^{2} = {(- 9)}^{2}$

Simplify each side of the equation.

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

${(z^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

Simplify the left side.

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

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

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

$z^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$z^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Rewrite the expression.

$z^{1} = {(- 9)}^{2}$

Simplify.

$z = {(- 9)}^{2}$

Simplify the right side.

Raise $- 9$ to the power of $2$ .

$z = 81$

Exclude the solutions that do not make $\sqrt{z} + 9 = 0$ true.

$No solution$