Question

given that √5 is irrational,prove that 2√5-3 is an irrational number ​

Answer 1

it is given that √5 is irrational..so.

2*√5-3

-1√5..if we multiply√5 which is irrational

by-1 then the answer will be irrational..so

2√5-3is also irrational no.

Answer 2

Answer:

Step-by-step explanation:

(Q) Given that √5 is irrational.

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

(Sol)->

Let us assume that 2√5-3 is a rational number.

i.e. 2√5-3 = p/q (where p and q are integers )

Now,

2√5-3 = p/q

2√5 = p/q +3

2√5 = (p+3q)/q

√5 = (p+3q)/2q

We can see that LHS is an irrational number which can never be equal to RHS which is a rational number. Therefore, our assumption that 2√5-3 is a rational number is wrong. 2√5-3 is not a rational number, it is an irrational number.

Hence proved.

Done!!