Answer: OPTION C.
Step-by-step explanation:
You have the expression:
[tex]\frac{\sqrt{75a}+\sqrt{12a}-\sqrt{27a}}{\sqrt{3a}}[/tex]
Descompose the numbers into its prime factors:
[tex]75=3*5*5=3*5^2[/tex]
[tex]12=2*2*3=2^2*3\\27=3*3*3=3^2*3[/tex]
Substitute and simplify
[tex]=\frac{\sqrt{3*5^2*a}+\sqrt{2^2*3*a}-\sqrt{3^2*3*a}}{\sqrt{3a}}[/tex]
[tex]=\frac{\sqrt{3*5^2*a}+\sqrt{2^2*3*a}-\sqrt{3^2*3*a}}{\sqrt{3a}}\\\\=\frac{5\sqrt{3a}+2\sqrt{3a}-3\sqrt{3a}}{\sqrt{3a}}\\\\=\frac{4\sqrt{3a}}{\sqrt{3a}}\\\\=4[/tex]
