Question

prove that root 5 is an irrational number. Hence show that 3 root 5 minus 8 is also an irrational number​

Answer 1

Prove

√5 is an irrational number

Let √5 be a rational number

√5 = p/q

Squaring on both the side

(√5)^2 = (p/q) ^2

5 = p^2/q^2

5q^2 = p^2

Therefore p^2 is a multiple of 5

P has a factor of 5.

P^2 /5 = q^2

Therefore, q^2 is a multiple of 5.q has a factor of 5.

Both p and q has a factor of 5 except 1. Therefore our consideration is wrong.

Hence it is an irrational number.

When any natural number added or subtracted must be an irrational number.

So it proves that 3√5 - 8 is also an irrational number.