Show that 3√2 is an irrational number
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yo!!!
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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!!☺️☺️✌️✌️
☺️
▶️QUESTION: Show that 3√2 is an irrational number.
⏬⏬SOLUTION⏬⏬
____________________________________________
✔️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.
____________________________________________
hope it helps!!☺️☺️✌️✌️
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6
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