Solve by Factoring square root of x-8=13

$\sqrt{x - 8} = 13$

Move $13$ to the left side of the equation by subtracting it from both sides.

$\sqrt{x - 8} - 13 = 0$

Add $13$ to both sides of the equation.

$\sqrt{x - 8} = 13$

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

${\sqrt{x - 8}}^{2} = 13^{2}$

Simplify each side of the equation.

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Multiply the exponents in ${({(x - 8)}^{\frac{1}{2}})}^{2}$ .

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

${(x - 8)}^{\frac{1}{2} \cdot 2} = 13^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

${(x - 8)}^{\frac{1}{2} \cdot 2} = 13^{2}$

Rewrite the expression.

${(x - 8)}^{1} = 13^{2}$

Simplify.

$x - 8 = 13^{2}$

Raise $13$ to the power of $2$ .

$x - 8 = 169$

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

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Add $8$ to both sides of the equation.

$x = 169 + 8$

Add $169$ and $8$ .

$x = 177$

Solve by Factoring square root of x-8=13

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