Adding Radical Expressions

You can only add radicals that have the same radicand (the same expression inside the square root).

Here's how to add them:

1) Make sure the radicands are the same. If not, you cannot add them.
2) Add the outside numbers
3) Keep the radicand (the inside) the same.

Let's examine a few examples.

1) $Adding radical expressions img 2$

Since the radicands match, all we have to do is add 3+4 and keep the $Adding radical expressions img 3$ the same.

2) $Adding radical expressions img 4$

There is an understood one in front of $Adding radical expressions img 5$ , so 5+1=5 and $Adding radical expressions img 5$ stays the same.

3) $Adding radical expressions img 6$

Don't let negatives through you off. -2-8=-10 and $Adding radical expressions img 7$ stays the same.

4) $Adding radical expressions img 8$

This one cannot be added since the radicands do not match. This is the final answer.

5) $Adding radical expressions img 9$

At first glance, it appears this one cannot be added. However, $Adding radical expressions img 10$ can be simplified.
$Adding radical expressions img 11$
$Adding radical expressions img 12$

Practice: Add the radicals.

1) $Adding radical expressions img 13$

2) $Adding radical expressions img 14$

3) $Adding radical expressions img 15$

4) $Adding radical expressions img 16$

5) $Adding radical expressions img 17$

Answers: 1) $Adding radical expressions img 18$ 2) $Adding radical expressions img 19$ 3) $Adding radical expressions img 15$ 4) $Adding radical expressions img 20$ 5) $Adding radical expressions img 21$

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