Example 11
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
Hence 3√2 is irrational
Hence proved

Made by

Davneet Singh

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.