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How do you simplify square root of 10^-6?

1 Answer

Sep 13, 2015

You can write it as $10^{- 3}$ $10^-3$ or $\frac{1}{1000}$ $1/1000$

Explanation:

Square root of a number $a$ $a$ is the same as $a^{\frac{1}{2}}$ $a^(1/2)$ , so you can write this number as:

${(10^{- 6})}^{\frac{1}{2}}$ $(10^(-6))^(1/2)$

If you have a number raised two a power twice, you can write it as one power, where the exponents are multiplied:

${(10^{- 6})}^{\frac{1}{2}} = 10^{- 6 \cdot (\frac{1}{2})} = 10^{- 3}$ $(10^(-6))^(1/2)=10^(-6*(1/2))=10^(-3)$

Finally if you would like to get rid of the exponent you have to remember that negative exponent can be rewritten as an inverse number, so you have:

$10^{- 3} = \frac{1}{10^{3}} = \frac{1}{1000}$ $10^(-3)=1/10^3=1/1000$

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