Question

show that root 5 is irrational​

Answer 1

Answer:

Step-by-step explanation is given in the pic provided

Answer 2

Answer:

Let us assume √5 is a rational number,

By the property of rational number,

√5 = p/q,  Where, p and q are distinct integers and q≠0,

⇒ √5 q = p

By squaring both sides,

⇒ 5 q² = p² ------(1)

⇒ 5 is the factor of p²,

⇒ 5 is a factor of p -----(2)

So, we can write, p = 5a

Where, a is any integer,

From equation (1),

5 q² = (5a)² ⇒ 5 q² = 25 a² ⇒ q² = 5a²

⇒ 5 is a factor of q²

⇒ 5 is a factor of q ------(3),

From equation (2) and (3),

p and q are not distinct,

Which is a contradiction,

Hence, our assumption is wrong,

√5 is an irrational number.

Hence, proved.