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Radicals Homework -- Simplifying Radicals

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides sample problems which develop concepts related to simplifying radicals.

Based on the generalization you wrote in #5 in the module "Some Very Important Generalizations", and given the fact that 4 × 2 = 8 4×2=8, we can simplify 8 8 as follows:

Table 1
8 = 4 × 2 8 = 4 × 2 (because 8 is the same thing as 4 × 2 4×2)
4 × 2 = 4 × 2 4 × 2 = 4 × 2 (this is where we use that generalization)
4 × 2 = 2 2 4 × 2 =2 2 (because 4 4 is the same thing as 2)

So, we see that 8 8 is the same thing as 2 2 2 2 .

Exercise 1

Find 8 8 on your calculator.

Exercise 2

Find 2 2 on your calculator.

Exercise 3

Double your answer to #2 on your calculator.

Exercise 4

So, did it work?

Exercise 5

Good! Then let’s try another one. Simplify 72 72 , using the same steps I took to simplify 8 8 .

Exercise 6

Check your answer on the calculator. Did it work?

Exercise 7

Oh yeah, one final question: what is x 16 x 16 ? How can you test your answer?

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