Question

prove that:-
√3 = √4​

Answer 1

Answer:

Step-by-step explanation:

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

Answer:

let √3+√4 be a rational number such that it can be written in the form of a/b where a and b are positive integers and co primes as well

therefore, √3+√4=a/b

squaring both sides

(√3+√4)²=(a/b)²

3+4+2√12=a²/b². (using identity (a+b)²=a²+b²

+2ab)

7+2√12=a²/b²

2√12=a²-7b²/b². (taking LCM here)

√12=a²-7b²/2b²

but as we know that √12 is irrational

so, this contradiction is arisen bcoz of our wrong assumption that √3+√4 is rational

so.. we conclude that √3+√4 is irrational