how to add, subtract radical terms: sqrt[3] + sqrt[4], etc

[Guest]

How would I subtract radicals and add them? Would they have to have the same root and the same coefficient? For instance, how would I add the square root radical of 3 and the square root radical of 4?

 

[skeeter]

\(\displaystyle \L \sqrt{3} + \sqrt{4} = \sqrt{3} + 2\)

that's as far as you can go.

look here for a lesson.

 

[pka]

In general, we can add any two real numbers.
But there may not be a neat and compact answer.
\(\displaystyle \sqrt 3 + \sqrt 4 = \sqrt 3 + 2\) and there is no further simplification.
But for \(\displaystyle \sqrt 3 + \sqrt 5\) there is no further simplification.
In some cases we can:
\(\displaystyle \begin{array}{rcl}
\sqrt 3 + \sqrt {12} & = & \sqrt 3 + \sqrt 4 \sqrt 3 \\
& = & \sqrt 3 + 2\sqrt 3 \\
& = & 3\sqrt 3 \\
\end{array}.\)

 

[Guest]

Thank you!