Solve for z square root of 5-z+3=6

$\sqrt{5 - z} + 3 = 6$

Move all terms not containing $\sqrt{5 - z}$ to the right side of the equation.

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Subtract $3$ from both sides of the equation.

$\sqrt{5 - z} = 6 - 3$

Subtract $3$ from $6$ .

$\sqrt{5 - z} = 3$

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

${\sqrt{5 - z}}^{2} = 3^{2}$

Simplify each side of the equation.

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

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

${(5 - z)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

${(5 - z)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(5 - z)}^{1} = 3^{2}$

Simplify.

$5 - z = 3^{2}$

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

$5 - z = 9$

Solve for $z$ .

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

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Subtract $5$ from both sides of the equation.

$- z = 9 - 5$

Subtract $5$ from $9$ .

$- z = 4$

Multiply each term in $- z = 4$ by $- 1$

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Multiply each term in $- z = 4$ by $- 1$ .

$(- z) \cdot - 1 = 4 \cdot - 1$

Multiply $(- z) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 z = 4 \cdot - 1$

Multiply $z$ by $1$ .

$z = 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$z = - 4$

Solve for z square root of 5-z+3=6

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