For this case we must simplify the following expression:
[tex]\frac {\sqrt {10x ^ 3}} {\sqrt {5x}}[/tex]
We combine the expression in a single radical:
[tex]\sqrt {\frac {10x ^ 3} {5x}} =[/tex]
We eliminate common factors of the numerator and denominator:
[tex]\sqrt {\frac {2x ^ 3} {x}} =\\\sqrt {2x ^ 2} =[/tex]
By definition of power properties we have to:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]\sqrt {2x ^ 2} = x \sqrt {2}[/tex]
Answer:
Option A
