Algebra Examples

$\frac{1}{\sqrt{1 - {(\frac{4}{5})}^{2}}}$

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $\frac{4}{5}$ .

$\frac{1}{\sqrt{1 - \frac{4^{2}}{5^{2}}}}$

Step 1.2

Raise $4$ to the power of $2$ .

$\frac{1}{\sqrt{1 - \frac{16}{5^{2}}}}$

Step 1.3

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

$\frac{1}{\sqrt{1 - \frac{16}{25}}}$

Step 1.4

Write $1$ as a fraction with a common denominator.

$\frac{1}{\sqrt{\frac{25}{25} - \frac{16}{25}}}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{1}{\sqrt{\frac{25 - 16}{25}}}$

Step 1.6

Subtract $16$ from $25$ .

$\frac{1}{\sqrt{\frac{9}{25}}}$

Step 1.7

Rewrite $\sqrt{\frac{9}{25}}$ as $\frac{\sqrt{9}}{\sqrt{25}}$ .

$\frac{1}{\frac{\sqrt{9}}{\sqrt{25}}}$

Step 1.8

Simplify the numerator.

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Step 1.8.1

Rewrite $9$ as $3^{2}$ .

$\frac{1}{\frac{\sqrt{3^{2}}}{\sqrt{25}}}$

Step 1.8.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{1}{\frac{3}{\sqrt{25}}}$

Step 1.9

Simplify the denominator.

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Step 1.9.1

Rewrite $25$ as $5^{2}$ .

$\frac{1}{\frac{3}{\sqrt{5^{2}}}}$

Step 1.9.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{1}{\frac{3}{5}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{5}{3})$

Step 3

Multiply $\frac{5}{3}$ by $1$ .

$\frac{5}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$