Fundamentals of Math

Fundamentals of Mathematics

Example 3.2.1

Find the √32 .

1. Decompose 32 by creating a factor tree.

2. Since the index is blank that means we are taking the “square root” of 32, so you need two identical numbers to create a pair. This pair is circled while the stand alone two is boxed in.

3. The pair comes outside the radical, and the isolated number stays inside.

Tip: Cross out your pairs and stand-alone numbers once you’ve taken care of them, so you do not forget any numbers.

4. Simplify is needed.

√32 = 4√2

Example 3.2.2

1. Decompose 54 by creating a factor tree.

2. Since the index is three that means we are taking the “cube root” of 54, so you need three identical numbers to create a group. This group is circled while the stand alone two is boxed in.

3. The pair comes outside the radical, and the isolated number stays inside.

Tip: Cross out your groups and stand-alone numbers once you’ve taken care of them, so you do not forget any numbers.

√54 3 = 3√2 3

4. Simplify is needed.

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