Grade 8 Irrational Numbers: Number Line

Worked examples

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

1. Example 1

   On a number line, which whole number is closest to √20?

   1. 4² = 16 and 5² = 25, so √20 is between 4 and 5.
   2. Halfway between them is 4.5, and 4.5² = 20.25. 20 is less than 20.25, so √20 is closer to 4.
   3. So the whole number closest to √20 is 4.

   Answer: 4

2. Example 2

   How many whole numbers are between √48 and √91 on a number line?

   1. √48 is between 6 and 7 (6² = 36 and 7² = 49).
   2. √91 is between 9 and 10 (9² = 81 and 10² = 100).
   3. The whole numbers between them: 7 through 9. That is 3 whole numbers.

   Answer: 3

3. Example 3

   Points are marked on a number line at 8.5, 8.8, 9.1 and 9.4. Which point is closest to √83?

   1. Square the points around it: 9.1² = 82.81 and 9.4² = 88.36, so √83 is between 9.1 and 9.4.
   2. Halfway between them is 9.25, and 9.25² = 85.5625. 83 is less than that, so √83 is closer to 9.1.
   3. The closest point is 9.1.

   Answer: 9.1