Grade 8 Irrational Numbers: Comparing Numbers

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   Which number is the greatest? Choices: √5 · 1.4 · 2.5 · √8

   1. Write each number as a decimal so they are easy to compare: √5 ≈ 2.24, 1.4, 2.5, √8 ≈ 2.83.
   2. From least to greatest: 1.4 < √5 < 2.5 < √8.
   3. The greatest is √8.

   Answer: √8

2. Example 2

   Which number is the least? Choices: 7.5 · √46 · 20/3 · 51/7

   1. Write each number as a decimal so they are easy to compare: 7.5, √46 ≈ 6.78, 20/3 ≈ 6.67, 51/7 ≈ 7.29.
   2. From least to greatest: 20/3 < √46 < 51/7 < 7.5.
   3. The least is 20/3.

   Answer: 20/3

3. Example 3

   Which is greater: 5.7 or √33?

   1. Both numbers are positive, so the one with the bigger square is bigger. Square both: 5.7² = 32.49 and (√33)² = 33.
   2. 33 > 32.49, so √33 > 5.7.
   3. So √33 is greater.

   Answer: √33