Question

prove that root 2+root 5 irrational​

Answer 1

Answer:

Given : 2 + √5

To prove : 2 + √5 is an irrational number.

Proof : Let 2 + √5 is a rational number i. e.

2 + √5 = a/b ( where a and b are co- prime number and are positive integer.)

Now,

2 + √5 = a/b

√5 = a/b - 2

√5 = a - 2b/b

Here a and b are positive integer i.e. (a-2b/b) is a rational number and also √5 is a rational number.

But we know that √5 is an irrational number.

i.e. 2 + √5 is an irrational number.

Hence, it is proven