Question

Simplify 6/sqrt 3 +2

Answer 1

\[\frac{ 6 }{ \sqrt{3}+2 } ?\]

Answer 2

multiply and divide by the conjugate that is \[\sqrt{3} - 2\]

Answer 3

and then solve as \[(6\div \sqrt{3}+2) *(\sqrt{3}-2 \div\sqrt{3} - 2)\]

Answer 4

yes, use conjugate.
(The purpose of it is to avoid the middle term, because what you will get in the denominator is something similar to " (a+b)(a-b)" which simplifies to "a^2-b^2" - without any middle term. The reason we are trying to avoid the middle term is because we can't have a radical in the denominator, but we will if we get any middle term.)

\(\huge\color{blue}{ \frac{ 6 }{ \sqrt{3} +2 } }\) follow me from here.

\(\huge\color{blue}{ \frac{ 6 }{ \sqrt{3} +2 } }\) \(\huge\color{red}{ \times \frac{ \sqrt{3}-2 }{ \sqrt{3} -2 } }\)

\(\huge\color{blue}{ \frac{ 6 ~\color{red} {(~\sqrt{3} -2~) } }{ (\sqrt{3} +2)~\color{red} {(~\sqrt{3} -2~) } } }\)

\(\huge\color{blue}{ \frac{6\sqrt{3}-12}{\sqrt{3}^2-\sqrt{2}^2} }\) for the bottom I used (a+b)(a-b)=a^2-b^2 and for the top just expended. Now, lets finish simplifying...

\(\huge\color{blue}{ \frac{6\sqrt{3}-12}{9-4}}\)

\(\huge\color{blue}{ \frac{6\sqrt{3}-12}{5}}\)


THAT'S THE SIMPLEST FORM \(\color{green}{ :)}\)