Question

Which choice is equivalent to the quotient shown here when x is greater than or equal to 0?

Answer 1

Answer: OPTION C

Step-by-step explanation:

Remember that:

$\sqrt[n]{a^n}=a$

And the Product of powers property establishes that:

$a^m*a^n=a^{(mn)}$

Rewrite the expression:

$\frac{\sqrt{18x} }{\sqrt{32} }$

Descompose 18 and 32 into their prime factors:

$18=2*3*3=2*3^2\\32=2*2*2*2*2=2^5=2^4*2$

Substitute into the expression, then:

$\frac{\sqrt{(2*3^2)x} }{\sqrt{2^4*2} }$

Finally,simplifying, you get:

$\frac{3\sqrt{(2)x} }{2^2\sqrt{2} }=\frac{3\sqrt{2x}}{4\sqrt{2}}=\frac{(3)(\sqrt{x})(\sqrt{2})}{(4)(\sqrt{2})}= \frac{3\sqrt{x}}{4}$