COMPARING RATIONAL AND IRRATIONAL NUMBERS

Example Problems on Comparing Rational and Irrational Numbers

Compare the following numbers using < or >.

Problem 1 :

√32 ___  5.1

Solution :

√32 ___5.1

√32 lies between √25 and √36.

5.1 is nearer to 5, so value of √32 will be greater than 5.1.

√32 > 5.1

Problem 2 :

√38 ____√42

Solution :

√38 ___√42

√38 lies between √36 and √49.

√38 < √42

Problem 3 :

√17___ 9/2

Solution :

√17____ 9/2

√17 lies between √16 and √25.

√16 = 4, then approximate value of √17 is 4.1...

9/2 = 4.5

4.1 < 4.5

√17 < 9/2

Problem 4 :

√49___ 7.1

Solution :

√49___7.1

√49 = √(7 × 7)

= 7

7 < 7.1

√49 < 7.1

Problem 5 :

√99 ____ 28/3

Solution :

√99 ____ 28/3

√99 lies between √81 and √100.

√99 is nearly √100, so approximate value of √99 is 9.9...

28/3 = 9.33

9.9 > 9.33

√99 > 28/3

Problem 6 :

√17 ___ 4.5

Solution :

√17 ____ 4.5

√17 lies between √16 and √25.

So, approximate value of √17 is 4.1... 

4.1 < 4.5

√17 < 4.5

Problem 7 :

43/5 _____√65

Solution :

43/5 ____ √65

43/5 = 8.6

√65 lies between √64 and √81.

√65 is nearly √64. So, its approximate value will be 8.1.....

8.6 > 8.062

43/5 > √65

Problem 8 :

√12 ___√21

Solution :

√12 ____√21

√12 lies between √9 and √16.

So, approximate value of √12 is 3..... 

√21 lies between √16 and √25.

So, approximate value of √21 is 4.....

3.464 < 4.582

√12 < √21

Problem 9 :

√16 ___ 3.9

Solution :

√16 ___  3.9

√16 = √(4 × 4)

= 4

4 > 3.9

Problem 10 :

√2 ___ 7/4

Solution :

√2 ___ 7/4

√2 lies between √1 and √3.

Approximate values of √2 is 1.414. 

7/4 = 1.75

1.414 < 1.75

Problem 11 :

√50 ___15/2

Solution :

√50 ___ 15/2

√50 lies between √49 and √64.

Approximate values of √50 is 7.07. 

15/2 = 7.5

7.07 < 7.5

Problem12 :

√9 ____3.01

Solution :

√9 ___3.01

√9 = √(3 × 3)

= 3

3 < 3.01

√9 < 3.01