Question

prove the root 5 is ireational​

Answer 1

let √5 be rational number.

√5 = p/q (where p and q are integers and q is not equal to zero)

Squaring both sides

(√5)² = (p/q)²

5 = p²/q²

5q² = p²

here we see that,

5 divide p

and

5 also divide p²......(¡)

Let p be 5

5q² = p²

putting p = 5

5q² = (5)²

5q² = 25

q² = 5

here we see that,

5 divide q

and

5 also divide q² .......(¡¡)

so, from (¡) and (¡¡)

we get

5 is a common factor of p and q.

so,

our assumption is wrong.

√5 is an irrational number.

Here is your answer....