What is the square root of 0.0025?

1 Answer
Mar 3, 2018

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad sqrt{ 0.0025 } \ = \ .05 \qquad.

Explanation:

"One way this can be done is by writing the number in"
"exponential form, then using properties of radicals and"
"exponents, as below:"

\qquad 0.0025 \ = \ .0025 \ = \ \underbrace{.0025}_{"4 places right of decimal point"} \ = \ 25 cdot 10^{-4}

:.\qquad \qquad 0.0025 \ = \ 25 cdot 10^{-4}

:. \qquad \ sqrt{ 0.0025 } \ = \ sqrt{ 25 cdot 10^{-4} } \qquad \qquad \ \ \ color{blue}{ "now use:" \quad sqrt{ab}=sqrt{a} cdot sqrt{b} }

\qquad \qquad \qquad \qquad \qquad \quad \ \ \ \ = \ sqrt{ 25 } cdot sqrt{ 10^{-4} }

\qquad \qquad \qquad \qquad \qquad \quad \ \ \ \ = \ 5 cdot sqrt{ (10^{-2} )^2 } \qquad \qquad \qquad \qquad \ color{blue}{ "now use:" \quad sqrt{a^2}=|a| }

\qquad \qquad \qquad \qquad \qquad \quad \ \ \ \ = \ 5 cdot |10^{-2}|

\qquad \qquad \qquad \qquad \qquad \quad \ \ \ \ = \ 5 cdot 10^{-2}

\qquad \qquad \qquad \qquad \qquad \quad \ \ \ \ = \ .05 \qquad.

"Thus:"

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad sqrt{ 0.0025 } \ = \ .05 \qquad.