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From Karnataka Open Educational Resources
→Hints for difficult problems
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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 =
−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 =
