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The Multiplication Property of Square Roots tells us that sqrt(ab)=sqrt(a) * sqrt(b), for a≥ 0 and b≥ 0. Moreover, the Division Property of Square Roots tells us that sqrt(ab)= sqrt(a)sqrt(b), for a≥ 0 and b≥ 0.
sqrt(2)/5 m^2
We want to simplify a radical expression. To do so we will assume that m>0, otherwise the given expression would not be defined.
sqrt(2m/25m^5)
Write as a sum
a^(1+m)=a*a^m
Cancel out common factors
Simplify quotient
sqrt(a/b)=sqrt(a)/sqrt(b)
sqrt(a* b)=sqrt(a)*sqrt(b)
Calculate root
Split into factors
a^(m* n)=(a^m)^n
sqrt(a^2)=a