Question

27. Show that 9 + √5 is an irrational number.​

Answer 1

Answer:

$\sqrt{5 } = 2.23606798$

is a irrational number

so 9 + 2.23606798 = 11.23606798

$so \: 9 + \sqrt{5} \: is \: a \: irrational$

Answer 2

Let 9+ √5 is a rational number.

9+√5 = a/b, b ≠ 0 …(i)

Where a and b co-prime integer number.

Equation (i) can be written as

√5 = a/b – 9 or √5

= (a - 9b)/b ….(ii)

Since, a and b are integers.

So (a - 9b)/b will be rational number, so from equation (ii)

we find that √5 is a rational number.

But we know that √5 is a irrational number..

So this result is contradicted.

So our hypothesis is wrong. Hence 9+ √5 is a irrational number.