Show that 3√2 is an irrational number. Created by Zayer. Math

Show that 3√2 is an irrational number...

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August 2021 2 57 Report

Show that 3√2 is an irrational number

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▶️QUESTION: Show that 3√2 is an irrational number.

⏬⏬SOLUTION⏬⏬

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✔️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

✔️Here, a/3b is a rational number but √2 is irrational

✔️Since, Rational ≠ Irrational.

✔️This is a contradiction.

✔️Therefore, our assumption is incorrect.

✔️Hence, 3√2 is irrational.

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hope it helps!!☺️☺️✌️✌️

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