Question

Proved that root 5 is irretional.

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Answer 1

Step-by-step explanation:

as 5 is not a square of any number so root 5 is irrational

Answer 2

To prove ✓5 is a rational number.

Let, ✓5 is rational number.

✓5= a/b ( a and b e belongs to integers,b is not equals to 0 and a and b are co- primes)

(✓5)^2 = (a/b)^2

→ 5 = a^2/b^2

→ 5b^2 = a^2

→ a^2 = 5b^2

→5|a^2

→ 5 divides a. ......... equation (1)

Let a=5m ( m belongs to integer)

→ (a)^2= (5m)^2

→a^2 = 25m^2

→ 5b^2 = 25m^2. ( a^2 =5b^2)

→ b^2= 25m^2/ 5

5m^2

→5|b^2

→ 5 divides b.. ......... equation (2)

From equation (1) and (2),

5 is the common factor of a and b but HCF of a and b is 1.

So, this contradicts our assumption that root 5 is not rational.

→ ✓5 is an irrational number.