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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
Solution
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.
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