Question

Proove that 3+root 2 is irrational

Answer 1

Let 3 + √2 be rational no.

3 +√2 = p/q ( where p and q are co-prime and q≠0)

√2 = p/q - 3

In RHS, there is rational no.

And in LHS, there is Irrational no.

This is not possible

This contradiction arise due to our wrong assumption.

⇒our assumption is wrong and 3+√2 is Irrational no.

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Answer 2

Answer:

LET US ASSUME THAT 3+ROOT 2 IS RATIONAL .

HENCE, 3+ ROOT 2 =A/B

ROOT 2 =1/3×A/B

ROOT 2 =A/3B

HENCE,A/ 3B IS RATIONAL BUT ROOT 2 IS IRRATIONAL.

AS IRRATIONAL CANNOT BE EQUAL TO RATIONAL.

SO, 3+ROOT 2 IS IRRATIONAL. ..

HOPE IT HELPS. . . . ☺☺