Question

prove that √2 is an irrational number ..


please explain in long form​

Answer 1

Answer:

A proof that the square root of 2 is irrational. Let's suppose √2 is a rational number. Then we can write it √2 = a/b where a, b are whole numbers, b not zero. We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction.

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Answer 2

Answer:

Step-by-step explanation:

let -/2 be a rational no.

-/2 = a/b --------- ( here a and b are co primes nos. )

Sqauring on both the sides

(-/2)^2 = (a/b)^2

2 = a^2/b^2

2b^2 = a^2

b^2 =a^2/2

2/a^2

2/a -------- ( 1)

a = 2c ------- ( where c is any integer)

a^2 = 2c^2

a^2 = 4c^2

2b^2 = 4c^2

b^2 = 4c^2 / 2

b^2 = 2 c^2

b^2/2 = c^2

2/b^2

2/b ------- (2)

:. From the above equation 1 and 2 this contradicts the fact the -/2 is a rational. This means our assumption was wrong

Hence, -/2 is an irrational no.

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