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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Example 7 Show that 3√2 is irrational. We have to prove 3√2 is irrational Let us assume the opposite, i.e., 3√𝟐 is rational Hence, 3√2 can be written in the form 𝑎/𝑏 where a and b (b≠ 0) are co-prime (no common factor other than 1) Hence, 3√𝟐 = 𝒂/𝒃 √2 " = " 1/3 " × " (𝑎 )/𝑏 " " √2 " = " (𝑎 )/3𝑏 √𝟐 " = " (𝒂 )/𝟑𝒃 Here, (𝑎 )/3𝑏 is a rational number But √2 is irrational Since, Rational ≠ Irrational This is a contradiction ∴ Our assumption is incorrect Therefore, 3√𝟐 is irrational Hence proved Therefore, 3√𝟐 is irrational Hence proved

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.