Precalculus Examples

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

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

Step 1

Rewrite

{\sqrt{x - 5}}^{2}

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

x - 5

$x - 5$ .

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Step 1.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{x - 5}

$\sqrt{x - 5}$ as

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

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

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

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

Step 1.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

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

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

Step 1.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

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

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

Step 1.4

Cancel the common factor of

2

$2$ .

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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.

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

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

Step 1.5

Simplify.

$x - 5 + 3$

$x - 5 + 3$

Step 2

Add

$- 5$ and

$3$ .

$x - 2$

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

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$