Activity - Irrational Numbers

Irrational numbers Exercise 1.3.1

1.Write four possible irrational numbers between 4 and 5.
Solution:
Consider the squares of 4 and 5
Square of 4 = 16 and Square of 5 = 25
We can also wright 4 and 5 as
√ 16 =4 and √ 25 =5
Between √ 16 and √ 25 there exists
√ 17 ,√ 18 , √ 19 , √ 20 , √ 21 , √ 22 , √ 23 , √ 24

2.Write four rational numbers between √ 2 and √ 3 Solution: root 2 ~1.414 and root 3 ~ 1.732 Rational numbers of root2 and root 3 is in between 1.4 to 1.7 like 1.45,1.5,1.55, 1.6 ........

3.Prove that √ 2 + √ 5 is an irrational number