of Poove thathumbes2 tus is an isrational

1.	of Poove thathumbes2 tus is an isrational
Answer» Let 2+√5 be a rational number. A rational number can be written in the form of p/q where p,q are integers. 2+√5 = p/q Squaring on both sides, (2+√5)² = (p/q)² 4+√5²+2(√5)(2) = p²/q² 4+5+4√10 = p²/q² 9+4√10 = p²/q² 4√10 = p²/q² - 9 √10 = (p²-9q²)/4q p,q are integers then (p²-9q²)/4q is a rational number. Then √10 is also a rational number. But this contradicts the fact that √10 is an irrational number. .°. Our supposition is false. 2+√5 is an irrational number. Hence proved.

Answer»

Let 2+√5 be a rational number.

A rational number can be written in the form of p/q where p,q are integers.

2+√5 = p/q

Squaring on both sides,

(2+√5)² = (p/q)²

4+√5²+2(√5)(2) = p²/q²

4+5+4√10 = p²/q²

9+4√10 = p²/q²

4√10 = p²/q² - 9

√10 = (p²-9q²)/4q

p,q are integers then (p²-9q²)/4q is a rational number.

Then √10 is also a rational number.

But this contradicts the fact that √10 is an irrational number.

.°. Our supposition is false.

2+√5 is an irrational number.

Hence proved.

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