Week 4 in Precalc 11

This week in math we learned how to add and subtract like radicals. This means that if there are like radicals in an equation, you can simplify their coefficients. In order to simplify their coefficients, you add or subtract. It is a very simple concept once you understand it! Here is an example:

3$\sqrt{2}$+2$\sqrt{2}$-6$\sqrt{2}$

= –$\sqrt{2}$

If the bases of the radicals aren’t the same then simplify the radicals to see if they are like radicals in simplified form. You can simplify radicals by finding the prime factorization of the number under the root sign and finding groups (depending on the index; index of two = group of two, index of three = group of three) and multiplying those numbers to form a perfect square. Then you can solve the perfect square so it is left as a coefficient next to the number under the root sign which is what’s left that can’t be solved. Here is an example:

$\sqrt{32}$+$\sqrt{8}$+3$\sqrt{2}$

=4$\sqrt{2}$+2$\sqrt{2}$+3$\sqrt{2}$

=9$\sqrt{2}$

Remember, all radicals must be in simplest form, only radicals with the same radicand can be combined and the coefficient changes but the radicand stays the same. I’ve included a more difficult example of a question solved below.