Question

√3+2 prove that irrational number

Answer 1

Answer:

Explanation:let 3-2√7 be an rational number.

then 3-2√7 = p/q

= - 2√7 = p/q - 3

= √7 = 3q - p/ 2q

as we know that, √7 is an irrational number

so our supposition is wrong that 3- 2√7 is a rational number.

hence, 3-2√7 is an irrational number

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Answer 2

Answer:

Explanation:

Let us assume that (√3+2) is a rational no.

√3+2=p/q, where p and q are co- primes.

2= (p/q)-√3

Squaring both sides,

4= p²/q²+3-2√3p/q

⇒ 2√3p/q=p²/q²-1

⇒√3=(p²-q²)q/2pq²

⇒√3=(p²-q²)/2pq

Since, p and q are integers, so , (p²-q²)/2pq is rational

Then, √3 is also rational

But this contradicts the fact that √3 is irrational. The contradiction arises when we assume that (√3+2) is rational.

∴ (√3+2) is irrational.[Proved]

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