PLOTTING IRRATIONAL NUMBERS ON A NUMBER LINE

Place a point on the number line given for each of the following irrational numbers.

Problem 1 :

Point A :√2

Solution :

Point A :√2

√2 lies between √1 and √3.

Approximate value of √2 is 1.414. 

So, the point 1.414 lies between 1.0 and 1.5.

Problem 2 :

Point B :√17

Solution :

Point B :√17

√17 lies between √16 and √25.

Approximate value of √17 is 4.1. 

So, the point 4.1 lies between 4 and 4.5.

Problem 3 :

Point C :√11

Solution :

Point C :√11

√11 lies between √9 and √16.

Approximate value of √11 is 3.3....  

So, the point 3.3 lies between 3.0 and 3.5.

Problem 4 :

Point D :√8

Solution :

Point D :√8

√8 lies between √2 and √9 and it is more nearer to √9.

Approximate value of √8 is 2.8

So, the point 2.8 lies between 2.5 and 3.0.

Problem 5 :

Point E :√5

Solution :

√5 lies between √2 and √9.

Approximate value of √5 is 2.24. 

So, the point 2.24 lies between 2.0 and 2.5.

Problem 6 :

Point V :√26

Solution :

Point V :√26

√26 lies between √25 and √36.

Approximate values of √26 is 5.1....

So, the point 5.1 lies between 5.0 and 5.5.

Problem 7 :

Point W :√88

Solution :

Point W : √88

√88 lies between √81 and √100.

Approximate value of √88 is 9.38. 

So, the point 9.4 lies between 9.0 and 9.5.

Problem 8 :

Point X :√77

Solution :

Point X :√77

√77 lies between √64 and √81.

Approximate value of √77 is 8.7. 

So, the point 8.7 lies between 8.5 and 9.0.

Problem 9 :

Point Y :√37

Solution :

Point Y : √37

√37 lies between √25 and √36.

Approximate value of √37 is 6.1

So, the point 6.1 lies between 6.0 and 6.5.

Problem 10 :

Point Z :√30

Solution :

Point z :√30

√30 lies between √25 and √36.

Approximate values of √30 is 5.3  

So, the point 5.3 lies between 5.0 and 5.5.