Simplify square root of (1-4/5)/2

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

Step 1

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

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Subtract $4$ from $5$ .

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{1}{5} \cdot \frac{1}{2}}$

Step 5

Multiply $\frac{1}{5} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{5}$ by $\frac{1}{2}$ .

$\sqrt{\frac{1}{5 \cdot 2}}$

Multiply $5$ by $2$ .

$\sqrt{\frac{1}{10}}$

Step 6

Rewrite $\sqrt{\frac{1}{10}}$ as $\frac{\sqrt{1}}{\sqrt{10}}$ .

$\frac{\sqrt{1}}{\sqrt{10}}$

Step 7

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{10}}$

Step 8

Multiply $\frac{1}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{1}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 9

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{\sqrt{10}}{\sqrt{10} \sqrt{10}}$

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{\sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}$

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{\sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{10}}{{\sqrt{10}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{10}}{{\sqrt{10}}^{2}}$

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\frac{\sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{10}}{10^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{10}}{10^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{10}}{10^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{10}}{10^{1}}$

Evaluate the exponent.

$\frac{\sqrt{10}}{10}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{10}}{10}$

Decimal Form:

$0.31622776 \dots$

Simplify square root of (1-4/5)/2

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