Precalculus Examples

${(\sqrt{x - 5})}^{2} + 3$

Step 1

Rewrite ${\sqrt{x - 5}}^{2}$ as $x - 5$ .

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 5}$ as ${(x - 5)}^{\frac{1}{2}}$ .

${({(x - 5)}^{\frac{1}{2}})}^{2} + 3$

Step 1.2

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

${(x - 5)}^{\frac{1}{2} \cdot 2} + 3$

Step 1.3

Combine $\frac{1}{2}$ and $2$ .

${(x - 5)}^{\frac{2}{2}} + 3$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Cancel the common factor.

${(x - 5)}^{\frac{2}{2}} + 3$

Step 1.4.2

Rewrite the expression.

${(x - 5)}^{1} + 3$

Step 1.5

Simplify.

$x - 5 + 3$

Step 2

Add $- 5$ and $3$ .

$x - 2$