What is (5 square root of 5) squared?

##(5sqrt5)^2 = 125##

Expressed as ##(5sqrt5)^2##.
Remember that ##a^m xx a^n = a^(m+n)##
Therefore, ##5^(1+1/2) = 5^(3/2)##
Also ##(a^m)^n = a^(mn)##
Hence, ##(5^(3/2))^2 = 5^(3/2 * 2) = 5^3##
##5## to the power of ##3## is ##5*5*5=125.##
Alternatively,
##(5sqrt5)^2 = 5^2 * (sqrt5)^2 = 25 * 5 = 125##

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