Question

Write a rational number between √2 and √7.

Answer 1

There are 2 methods

1. Take the approximate values of root 5 and root 7 and find the irrational numbers between them

Root 5 = 2.23

Root 7 = 2.64

2 values between them are

2.333356282581......

2.5815830267199.....

2. If a^2 < m^2 < b^2

a a^2 =(Root5)^2

b^2 =( Root7)^2

And m are the numbers we need to find

So m^2 lies between 5 and 7

Take any 2 values

Example - 6 and 6.5

So m = Root 6 and root 6.5

(You can take others too)

Answer 2

√2 =1.414........

√7 = 2.645......

Thus a rational number between √2 and √7 = 1/2(1.4+2.6 )= 1/2(5)=2.5