Answer: OPTION C
Step-by-step explanation:
Remember that:
[tex]\sqrt[n]{a^n}=a[/tex]
And the Product of powers property establishes that:
[tex]a^m*a^n=a^{(mn)}[/tex]
Rewrite the expression:
[tex]\frac{\sqrt{18x} }{\sqrt{32} }[/tex]
Descompose 18 and 32 into their prime factors:
[tex]18=2*3*3=2*3^2\\32=2*2*2*2*2=2^5=2^4*2[/tex]
Substitute into the expression, then:
[tex]\frac{\sqrt{(2*3^2)x} }{\sqrt{2^4*2} }[/tex]
Finally,simplifying, you get:
[tex]\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}[/tex]
