http://www.mathwarehouse.com/algebra/radicals/how-to-add-square-roots.php
see if this video helps
+50 say i had a radical 5 and a radical 8 i didnt know if i could add those together
+9673 If a and b have a common non-square-number factor**, and the square root of the 2 cannot be simplified into a whole number, then \(\sqrt a\) and \(\sqrt b\) can be added together!!
Your question is \(\sqrt{5} + \sqrt 8\), because 5 and 8 does not have a common non-square-number factor**, they cannot be added together. The answer is:
\(\quad\sqrt 5 + \sqrt 8 \\ =\sqrt 5 + \sqrt{2^2\cdot 2}\\ =\sqrt 5 + \sqrt{2^2} \cdot \sqrt2\\ =\sqrt 5 + 2\sqrt 2\)
Let's say \(\sqrt 8 + \sqrt {32}\), 8 and 32 have a common non-square-number factor** 2, so they can be added together. The answer is:
\(\quad \sqrt8 + \sqrt{32}\\ =\sqrt{2^2\cdot 2}+\sqrt{2^4\cdot 2}\\ =\sqrt{2^2}\cdot \sqrt2 + \sqrt{2^4}\cdot \sqrt2\\ =2\cdot \sqrt2 + 2^2 \cdot \sqrt2\\ =2\sqrt2 + 4\sqrt2\\ =6\sqrt2\)
**: common non-square-number factor here means common factor that are not square numbers(i.e. 1,4,9,16,25,36,49,.....)
