Question

Prove that 3 - root5 is an irrational​

Answer 1

Answer:

value of √5 is irrational which is 2.236067977499789...

so if we subtract it from 3 then we will have

1.236067977499789...

which is also an irrational

hence proved

Answer 2

Answer:

Let us assume that 3+

5

is a rational number.

Now,

3+

5

=

b

a

[Here a and b are co-prime numbers]

5

=[(

b

a

)−3]

5

=[(

b

a−3b

)]

Here, [(

b

a−3b

)] is a rational number.

But we know that

5

is an irrational number.

So, [(

b

a−3b

)] is also a irrational number.

So, our assumption is wrong.

3+

5

is an irrational number.

Hence, proved.