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Real numbers
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Revision as of 06:19, 23 February 2014
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06:19, 23 February 2014
→Hints for difficult problems
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= Hints for difficult problems =
= Hints for difficult problems =
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Irrational numbers
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Exercise 1.3.1
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1.Write four possible irrational numbers between 4 and 5.
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Solution:
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Consider the squares of 4 and 5
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42 = 16 and 52 = 25
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We can also wright 4 and 5 as
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=4 and =5
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Between and there exists
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,,,,,,,
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2.Write four rational numbers between and
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Solution:
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root 2 ~1.414 and
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root 3 ~ 1.732
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Rational numbers of root2 and root 3 is in between 1.4 to 1.7 like 1.45,1.5,1.55, 1.6 ........
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3.Prove that + is an irrational number
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Solution:
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Let us assume on contrary that is a rational number.
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Then there exists co-prime positive integers p and q such that
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=
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-=
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(-)2 = ()2
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+2- 2.= 5
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=
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p and q are integers
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is rational
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But this contradicts the fact that is irrational.
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So, our assumption is wrong.
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Hence, is irrational
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Write an irrational
= Project Ideas =
= Project Ideas =
Radha
499
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