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Last updated at May 29, 2018 by Teachoo
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Example 10 Show that 5 - 3 is irrational. We have to prove 5 - 3 is irrational Let us assume the opposite, i.e., 5 - 3 is rational Hence, 5 - 3 can be written in the form / where a and b (b 0) are co-prime (no common factor other than 1) Hence, 5 - 3 = / 3 = / - 5 3 = ( 5 )/ 3 = ( 5 )/ 3 = (( 5 )/ ) 3 = (5 )/ Here, ( +5 )/ is a rational number But 3 is irrational Since, Rational Irrational This is a contradiction Our assumption is incorrect Hence, 5 - 3 is irrational Hence proved.
Examples
Example 2 Not in Syllabus - CBSE Exams 2021
Example 3 Not in Syllabus - CBSE Exams 2021
Example 4 Important Not in Syllabus - CBSE Exams 2021
Example 5 Important
Example 6
Example 7
Example 8
Example 9 Important
Example 10 You are here
Example 11
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