Question

The product of the square root of x with the cube root of x is

Options

•  cube root of the square root of x

• sixth root of the fifth power of x

•  fifth root of the sixth power of x

• sixth root of x

Answer 1

We have to find the product (say L) of the square root of x with the cube root of x is. So, 

`L = 2sqrtx xx 3sqrtx`

`= x^(1/2) xx x ^(1/3)`

`= x^(1/2+1/3)`

`= x^((1xx3)/(2xx3)+(1xx2)/(3xx2))`

\[= x^\frac{3 + 2}{6} = x^\frac{5}{6}\]

The product of the square root of x with the cube root of x is `x^(5/6)`

Hence the correct alternative is  b.