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Adding Radicals

Q: How do I add radicals like this: ?

A: = =

Note that this is analogous to 2x + 4x = 6x, where the terms act similar to the variable x.

Let’s look at some more examples:

= =

Adding Unlike Radicals

Q: What if I have to add radicals, but the radicals are different? I am trying to add .

A: You can’t add those, or simplify any further without a calculator. You just have to leave it as it is, because the square roots are different (3 and 5).

=

Let’s look at . . . → Read More: Adding Unlike Radicals

Subtracting Radicals

Q: How do I subtract radicals like this: ?

A: Subtracting radicals is very similar to adding radicals.

= =

Rationalize the denominator

Q: Simplify the radical expression by rationalizing the denominator: . Thanks.

A: First let’s simplify the bottom, by splitting the up into /  (note that = 1)

To rationalize the denominator, you just multiply by . You are allowed to do this because really you are just multiplying by 1.

Note . . . → Read More: Rationalize the denominator