Question

Prove
that is root5 irrational​

Answer 1

Answer:Value of root is in decimal and it is a prime number

Value of root 5 is 2.236

Step-by-step explanation:

Answer 2

Answer:

Hi

Step-by-step explanation:

Let us prove √5 by contradiction.

Let us suppose that √5 is irrational.It means that we have co-prime integers a and b (b≠0) such that

√5=a/b

⇒b√5=a

squaring on bothsides,we get

⇒5b²=a²→→→→→1

It means that 5 is factor of a²

Hence,5 is also factor of a by theorem 2→→→→→2

If,5 is a factor of a,it means that we can write a=5c for some integer c.

Substituting value of a in 1

5b²=25c²⇒b²=5c²

It means that 5 is factor of b²

Hence,5 is also factor of b by theorem 3→→→→→3

From equation 2 and 3,we can say that 5 is factor of both a and b

But,a and b are co-primes

∴Out assumption was wrong,√5 cannot be rational,hence it is irrational.

∴Please mark it as brainlist answer