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# Week 4 in PreCalc 11

What I’ve learned this week is about adding and subtracting radicals.

But before that, we need to know the parts of a radical.

$\sqrt[n]{x}$ ,where n is the index and x is the radicand.

Radicals too, can be added together just like those regular numbers. It’s like adding a fraction, but first you need to make sure your index and your radicand are the same, just like how you need to have the same denominator when adding fractions.

REMEMBER: You CANNOT add radicals that DON’T HAVE THE SAME radicands AND index! It’s basically adding “like terms.”

E.g.

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

in words, having 2 copies of

$\sqrt{25} + \sqrt{9}$

Don’t panic. See if they simplify to a whole number.

$\sqrt{25} + \sqrt{9}$ $= 5 + 3$ $= 8$

Next thing is how to add radicals that don’t have the same radicands.

Note: this might not work for some of them if they have been simplified in their simplest form.

The only thing you need to do is to make them have the same radicands by factoring them. It’s based on the index that you have. For example, if your index is two, then you have to find perfect squares such as 4, 9, 16, … and if you have 3 as your index, then find perfect cubes such as 8, 27, … and so on.

For example:

$\sqrt{27} - \sqrt{3}$ $= \sqrt{9 x 3} - \sqrt{3}$ $= 3\sqrt{3} - \sqrt{3}$ $= 2\sqrt{3}$