Calculus Examples

${(\sqrt{5^{2} - 4})}^{2}$

Step 1

Simplify the expression.

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Step 1.1

Raise $5$ to the power of $2$ .

${\sqrt{25 - 4}}^{2}$

Step 1.2

Subtract $4$ from $25$ .

${\sqrt{21}}^{2}$

Step 2

Rewrite ${\sqrt{21}}^{2}$ as $21$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{21}$ as $21^{\frac{1}{2}}$ .

${(21^{\frac{1}{2}})}^{2}$

Step 2.2

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

$21^{\frac{1}{2} \cdot 2}$

Step 2.3

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

$21^{\frac{2}{2}}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$21^{\frac{2}{2}}$

Step 2.4.2

Rewrite the expression.

$21^{1}$

Step 2.5

Evaluate the exponent.

$21$