Page 29 - ArithBook5thEd ~ BCC

√
The side length of the middle square is a number which, when squared, yields 5, that is, 5. We can
√ √ √
see that 5is bigger than 4= 2, and less than 9= 3.
In general, if a whole number lies between two perfect squares, its square root must lie between the
two corresponding square roots.
√ √
Example 21. Since 21 lies between the perfect squares 16 and 25, 21 must lie between 16 = 4 and
√
25 = 5.
√
Example 22. Between what two consecutive whole numbers does 53 lie?

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Solution. Since 53 lies between the perfect squares 49 and 64, the square root 53 must lie between
√ √
49 = 7 and 64 = 8.

1.4.4 Exercises

Find the square roots:
√
1. 49
√
2. 81
√
3. 169
√
4. 121

√
5. 64
Between what two consecutive whole numbers do the following square roots lie?

√
6. 19
√
7. 75
√
8. 26
√
9. 32

10. Complete the square-root table:
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0= =6 =12 =18
√
1= =7 =13 =19
√
4= =8 =14 =20
√
9= =9 =15 =30
=4 =10 =16 =40
=5 =11 =17 =50

1.5 Division of Whole Numbers

How many times does 23 “go into” 100? Put another way, starting with 100, how many times can we
subtract 23 without obtaining a negative number? The answer is easily seen to be 4. Moreover, it is

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