Question

How do you solve `x^(3/2) = 27`?

Answer 1

`x=9.`

Explanation:

Given Eqn. : `x^(3/2)=27.`
`:.{x^(3/2)}^2=27^2.`
`:. x^{3/2*2}=(3^3)^2.`
`:.x^3=3^(3*2)=3^6=(3^2)^3.`
As powers are same, so must be the bases, so, `x=3^2=9.`

It can be easily verified that the root found satisfies the given eqn. Hence, the Soln. is `x=9.`