Question

prove √5 as irrational​

Answer 1

Let us assume opposite,

√5 is rational.

According to the question :

Form = p / q , where q is not equal to 0.

√5 = p / q

squaring both sides,

=> 5 = p^2 / q^2

=> 5q^2 = p^2

• p is divisible by 5.
• p = 5k , k is a positive integer.

squaring both sides,

=> 5q^2 = 5 × 5k^2

=> 5q^2 = 25k^2

substituting 5q^2 = p^2

=> 5q^2 = 25k^2

=> q^2 = 5k^2

• q is divisible by 5.
• p and q have common factor 5.
• p and q are co - primes.

=> So, √5 is an irrational number.

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