How do you write 5x^(5/2) as a radical form?

1 Answer
Apr 23, 2016

5sqrt(x^5) or 5x^2sqrt(x)

Explanation:

If x >= 0 then:

5x^(5/2) = 5x^(5*1/2) = 5(x^5)^(1/2) = 5sqrt(x^5)

If you prefer:

5x^(5/2) = 5x^(2+1/2) = 5x^2x^(1/2) = 5x^2sqrt(x)

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Footnote

Fractional exponents like this tend to work well with non-negative numbers, but can misbehave horribly for negative or Complex numbers.

For example:

(-1)^(3/2) = -i != i = ((-1)^3)^(1/2)

or even:

((-1)^(3/2))^(2/3) = (-i)^(2/3) = 1/2-sqrt(3)/2i != -1 = (-1)^(3/2 * 2/3)