Question

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

Answer 1

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Answer 2

✔️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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