Evaluate square root of 10^-6

$\sqrt{10^{- 6}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\sqrt{\frac{1}{10^{6}}}$

Step 2

Raise $10$ to the power of $6$ .

$\sqrt{\frac{1}{1000000}}$

Step 3

Rewrite $\sqrt{\frac{1}{1000000}}$ as $\frac{\sqrt{1}}{\sqrt{1000000}}$ .

$\frac{\sqrt{1}}{\sqrt{1000000}}$

Step 4

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{1000000}}$

Step 5

Simplify the denominator.

Rewrite $1000000$ as $1000^{2}$ .

$\frac{1}{\sqrt{1000^{2}}}$

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

$\frac{1}{1000}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{1000}$

Decimal Form:

$0.001$