Question

Simplify √75a+ √12a - √27a

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√3a
a) 1/4
B)-4
C)4

Answer 1

Answer: OPTION C.

Explanation:

You have the expression:

`(√(75a)+√(12a)-√(27a))/(√(3a))`

Descompose the numbers into its prime factors:

`75=3*5*5=3*5^2`

`12=2*2*3=2^2*3\\27=3*3*3=3^2*3`

Substitute and simplify

`=(√(3*5^2*a)+√(2^2*3*a)-√(3^2*3*a))/(√(3a))`

`=(√(3*5^2*a)+√(2^2*3*a)-√(3^2*3*a))/(√(3a))\\\\=(5√(3a)+2√(3a)-3√(3a))/(√(3a))\\\\=(4√(3a))/(√(3a))\\\\=4`