Question

given that ✓5 is an irrational number,prove that (3-✓5) is an irrational number

Answer 1

let us assume that (3-√5) is a rational number.

$3 - \sqrt{5} = \frac{p}{q}$

where p and q are integers

$\sqrt{5} = 3 - \frac{p}{q} \\ \sqrt{5} = \frac{3q -p }{q}$

here 3, p and q are integers so 3q-p/q is a rational number. so √5 is also a rational number. but it is given that √5 is an irrational number and it contradicts the fact also. therefore our assumption is wrong.
(3-√5) is an irrational number

hence proved.

hope it helps you :)

#puja

Answer 2

Answer:

3-√5 is irrational number because they gave that √5 is a irrational number if a irrational number is multiplied, added, subtracted or divided it will be irrational number