Simplify the following: \sqrt{(15x)/(x^(3) ) } \frac{\sqrt{x^(2) } }{\sqrt{x^(3) } }

Question

Simplify the following:


`\sqrt{(15x)/(x^(3) ) }`

`\frac{\sqrt{x^(2) } }{\sqrt{x^(3) } }`

Answer 1

`\sqrt{ \frac{15x}{ {x}^(3) } }= \sqrt{ \frac{15}{ {x}^(2) } } = \frac{ √(15) }{ \sqrt{ {x}^(2) } } = ( √(15) )/(x) \\`

(√15)/x is the right answer.

`\frac{ \sqrt{ {x}^(2) } }{\sqrt{{x}^(3)}} = \frac{ {x}^{ (2)/(2) } }{ {x}^{ (3)/(2)}}= \frac{x}{ {x}^{(1 + (1)/(2)) } } = \frac{x}{x * {x}^{ (1)/(2) } } = (1)/( √(x) ) \: \\`

1/(√x) is the right answer.

Answer 2

For the first question:

`\sqrt{(15x)/(x^3)}\\= \sqrt{(15)/(x^2)}\\= (√(15))/(x)\\`

And the second

`(√(x^2))/(√(x^3))\\= (x^2)^{(1)/(2) }(x^3)^{(-1)/(2) }\\= x^1 * x^{(-3)/(2) }\\= x^{(2)/(2)} * x^{(-3)/(2) }\\= x^{-(1)/(2)}\\= (1)/(√(x))`