Question

Prove that √2+√3 is irrational only one will be given

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Answer 1

Answer:

We assume that 2 + √3 is a rational number. => 2 + √3 = p/q , where p & q are integers, 'q' not = 0. => here, LHS √3 is an irrational number. ... => RHS (p- 2q)/q is a rational number.

Answer 2

Answer:

Let √2 + √3 = (a/b) is a rational no

. On squaring both sides ,

we get 2 + 3 + 2√6

= (a2/b2) So,5 + 2√6 = (a2/b2) a rational no.

So, 2√6 = (a2/b2) – 5

Since, 2√6 is an irrational no. and (a2/b2) – 5 is a rational no.

So, my contradiction is wrong. So, (√2 + √3) is an irrational no.

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