Question

simplify the following:
$\sqrt{\frac{15x}{x^{3} } }$
$\frac{\sqrt{x^{2} } }{\sqrt{x^{3} } }$

Answer 1

Answer:

For the first question:

$\sqrt{\frac{15x}{x^3}}\\= \sqrt{\frac{15}{x^2}}\\= \frac{\sqrt{15}}{x}$

And the second

$\frac{\sqrt{x^2}}{\sqrt{x^3}}\\= (x^2)^{\frac{1}{2} }(x^3)^{\frac{-1}{2} }\\= x^1 \times x^{\frac{-3}{2} }\\= x^{\frac{2}{2}} \times x^{\frac{-3}{2} }\\= x^{-\frac{1}{2}}\\= \frac{1}{\sqrt{x}}$

Answer 2

Answer:

$\sqrt{ \frac{15x}{ {x}^{3} } }= \sqrt{ \frac{15}{ {x}^{2} } } = \frac{ \sqrt{15} }{ \sqrt{ {x}^{2} } } = \frac{ \sqrt{15} }{x}$

(√15)/x is the right answer.

$\frac{ \sqrt{ {x}^{2} } }{\sqrt{{x}^{3}}} = \frac{ {x}^{ \frac{2}{2} } }{ {x}^{ \frac{3}{2}}}= \frac{x}{ {x}^{(1 + \frac{1}{2}) } } = \frac{x}{x \times {x}^{ \frac{1}{2} } } = \frac{1}{ \sqrt{x} } \:$

1/(√x) is the right answer.