Question

provethat root 5
is irration​

Answer 1

Answer:

Refer the attachment

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Answer 2

Step-by-step explanation:

Let √5 be a rational number which is of the form p/q where p&q are co prime (q is not equal to 0)

Now,

√5 = P/q

Squaring both sides

√5^2 = (p/q)^2

5 = p^2/q^2

5q^2 = p^2

q^2 = p^2/5 -(i)

p^2 is divisible by 5

also, p is divisible by 5

Now,

let p = 5m for some integer

Putting p = 5m in eqn (i) , we get

q^2 = ( 5m)^2/5

q^2 = 25m^2/5

q^2 = 5m^2

m^2 = q^2/5

q^2 is divisible by 5

q is also divisible by 5 (ii)

From eqn (i) & (ii), we conclude that p&q have 5 in common factor.

But, it contradicts the fact that p&q are co prime

So, our assumption is wrong

Hence, √5 is an irrational number.