Question

Q4 Prove that 2- 3√5 is an irrational number. ​

Answer 1

let √5 be rational no.

I. e

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

q not equal to 0, p and q should be coprime

p=√5q

sq.on both sides

p^2 =5q^2

i.e 5 is the factor of the p

let p be m

(5m)^2= 5q^2

5m^2 =q^2

i.e 5 is the factor of q

but p and q should be coprime

so our supposition is wrong

i.e√5 is an irrational no.

as we know that

r+i.r= i.r

r-i.r=i.r

so 2-3√5 is an irrational no

hence proved

hope this will help you and marks it as brainlist plzzzzzzzzz

Answer 2

Please mark me Brainlist and Follow me.