Fundamentals of Math

Fundamentals of Mathematics

Practice 3.1.2

Directions: Simplify the following expressions (do not actually solve).

1. 8 3 × 8 2

2. 3 4 3 9 4. 9 5 9 2 6. 6 27 6 15

3. (7 3 )(7 4 )

5. (2 5 )(2 2 )

7. (7 11 ) 3

8. (2 24 ) 8

7

2

9. ( 2 3

10. ( 4 5

)

)

Answer Key on Page 119

3.2 Square and Cube Roots A radical , or root of a number, is a number ( ) , which when multiplied by itself a given number of times equals ( ) . A radical is comprised of three parts: an index, radical symbol, and radicand. The index tells you the number of times the radicand is multiplied by itself. The radicand is the thing you are finding the root of, and the radical symbol ( √ ) means "root of." It is essential to note the length of the horizontal bar is crucial because it indicants everything underneath the bar is the radicand. Also note, if no index is written then it is assumed to be 2.

Simplifying Radicals Ideally, you would decompose a radical into perfect squares (or cubes depending on the index), but that is not always possible. Therefore, the simplest method is to create a factor tree of your radicand. Then create groupings based on the pairs (number required per pair is determined by the index). Pairs come outside the radical and are multiplied together (if more than one), and unpaired numbers stay inside the radical and multiplied back together.

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