Question

prove 2 in a irrational​

Answer 1

Answer:

2 is a irrational number

Step-by-step explanation:

we can write root2=a/b. whereas a,b are whole number but not zero and a,b is the lowest term .so, 2 is a irrational number

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Answer 2

Answer:

lets just consider root 2 is rational which can be written in the form p/q.

Root 2 = p/q

squaring both sides :

(root 2)^2 = (p/q)^2

2= p^2/q^2

2q^2 = p^2 - (eq. 1)

q^2 = p^2/2

2 divides p^2

also 2 divides p

now , let p= 2c ( c is an integer )

we get 2q^2 = (2c)^2

2q^2 = 4c^2

q^2 = 4c^2/2

q^2 = 2c^2

q^2/2 = c

2 divides q^2

also 2 divides q

Thus, we find that 2 us a common factor of both p and q whixb controdicts that p and q are co prime.

therefore, our assumption is wrong.

so Root 2 is an irrational number.