Question

. Prove that √5 is irrational number.​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

let √5 be a rational number

then it must be in the form p/q where p≠0

(p and q are co-prime)

√5=p/q

√5×q=p

squaring on both sides

5q²=p²-------(1)

p² is divisible by 5

so p is divisible by 5

p=5x

squaring on both sides

p²=25x²

put it in equation (1)

5q²=25(x)²

q²=5x²

so q is divisible by 5

Thus p and q have a common factor of 5

So, there is a contradiction as per our assumption

We have assumed p and q are co-prime but here they a common factor of 5.

The above statement contradicts our assumption.

Therefore,√5 is an irrational number