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Line 145: − + − + + + + − 42 = 16 and 52 = 25+ − + − + + + − ,,,,,,, − 2.Write four rational numbers between and + − 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 + is an irrational number − Solution: − Let us assume on contrary that is a rational number. − Then there exists co-prime positive integers p and q such that − = − -= − (-)2 = ()2 − +2- 2.= 5 − = − p and q are integers − is rational − − But this contradicts the fact that is irrational. − So, our assumption is wrong. − Hence, is irrational − Write an irrational
→Hints for difficult problems
= Hints for difficult problems =
= Hints for difficult problems =
Irrational numbers
Irrational numbers<br>
Exercise 1.3.1
Exercise 1.3.1<br>
1.Write four possible irrational numbers between 4 and 5.
1.Write four possible irrational numbers between 4 and 5.
Solution:
Solution:
Consider the squares of 4 and 5
Consider the squares of 4 and 5
Square of 4 = 16 and Square of 5 = 25
We can also wright 4 and 5 as
=4 and =5
We can also write 4 and 5 as
√ 16 =4 and √ 25 =5
Between and there exists
Between and there exists
√ 17 ,√ 18 , √ 19 , √ 20 , √ 21 , √ 22 , √ 23 , √ 24
= Project Ideas =
= Project Ideas =