Simplify ^3 sqrt 5 • sqrt 2

I assume that we want to simplify:

( √5*√2)^3

Remember that:

√a*√b = √(a*b)

(a^n)^m = a^(n*m)

and:

√a = (a)^(1/2)

Then we can rewrite:

( √5*√2)^3 = (√5*2)^3 = (√10)^3

                                     = (10^(1/2))^3 = 10^(3/2)

We could keep simplifying this if we know that:

10^3 = 1000

Then:

10^(3/2) = (10^3)^(1/2) = (1000)^(1/2) = √1000

We can not simplify this anymore.

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step-by-step explanation:

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