Question

how do you simplify √((36-9x^2) / 4) ?

Answer 1

\[\sqrt{\frac{ 36-9x^2 }{ 4 }}\]

Answer 2

i used a calculator and it says \[\frac{ 3\sqrt{4 - x ^{2}} }{2 }\]
but i don't know why.

Answer 3

never use a calculator when it comes to this stuff they are dumb you just have to use your brain oh and @mathstudent55 I still need your help

Answer 4

\(\LARGE\sqrt{\frac{ 36-9x^2 }{ 4 }}\)

First, you can separate the numerator and the denominator by putting each one inside a root symbol.

\(\LARGE \frac{ \sqrt{36-9x^2} }{\sqrt{ 4 }} \)

The denominator is trivial:

\(\LARGE \frac{ \sqrt{36-9x^2} }{2} \)

Now work on the numerator by factoring a common factor. The GCF of the two terms is 9.

\(\LARGE \frac{ \sqrt{9(4-x^2)} }{2} \)

Now you can separate the two roots in the numerator:

\(\LARGE \frac{ \sqrt{9}\sqrt{4-x^2} }{2} \)

This now becomes:

\(\LARGE \frac{ 3\sqrt{4-x^2} }{2} \)

This is what you got.

Answer 5

:O ahh that makes sense. Thank you!