What is the square root of 0.0025?

Question

Abigail Allen · Accepted Answer

undefined The square root of 0.0025 is 0.05.

Abigail Allen · Answer

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