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Example 10 - Chapter 1 Class 10 Real Numbers (Term 1)

Last updated at Aug. 2, 2021 by

Example 10 - Show that 5 - root 3 is irrational - Chapter 1 - Examples

Example 10 - Chapter 1 Class 10 Real Numbers - Part 2
Example 10 - Chapter 1 Class 10 Real Numbers - Part 3

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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.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.