Question

prove that √3+√4 is irrational.​

Answer 1

Ello user !!!!!!

Here is your answer,

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Lets assume that :

√3 + √4 is rational.

√3 + √4 = r , where r is rational

Squaring both sides , we get

[√3 + √4 ]² = r²

3 + 2√12 + 4 = r²

7 + 2√12 = r²

2√12 = r² - 6

√12 = [ r² - 6] / 2

R.H.S is purely rational , whereas , L.H.S is irrational.

This is a contradiction.

This means that our assumption was wrong.

Hence , √3 + √4 is irrational.

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Answer 2

hope it helps

3 is a prime number. All primes, when rooted, are irrational numbers. Therefore √3 is irrational. √4 is 2. ANYTHING plus an irrational number has an answer that is still irrational. Therefore 2 + √3 = irrational.

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