Question

Q. Show that √7 is irrational.

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Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let is assume that√7 is rational number

Now, let √7 = a/b {where a and b are co-primes, b is not equal to 0}

Squarring both sides

(√7)² = (a/b)²

7 = a²/b²

b² = a²/7

a² is divisible by 7

therefore, a is also divisible by 7

let a = 7m for some integers

√7 = a/b

√7 = 7m/b

Squarring both sides

(√7)² = (7m/b)²

7 = 49/b²

m² = b²/7

b² is divisible by 7

therefore, b is also divisible by 7

therefore, a nd b have atleast 7 as a common factor

But this contradict the fact that a and b are co-primes

√7 is a rational number, this contradiction arises that

√7 is irrational

This contradict our assumption that is wrong.