Ex 1.2, 3 (ii) - Chapter 1 Class 10 Real Numbers

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Ex 1.2, 3 Prove that the following are irrationals : (ii) 7√5 We have to prove 7√5 is irrational Let us assume the opposite, i.e., 7√𝟓 is rational Hence, 7√5 can be written in the form 𝑎/𝑏 where a and b (b≠ 0) are co-prime (no common factor other than 1) Hence, 7√𝟓 = 𝒂/𝒃 √5 " = " 1/7 " × " (𝑎 )/𝑏 " " √𝟓 " = " (𝒂 )/𝟕𝒃 Here, (𝑎 )/7𝑏 is a rational number But √5 is irrational Since, Rational ≠ Irrational This is a contradiction ∴ Our assumption is incorrect Therefore, 7√𝟓 is irrational Hence proved