Question

show that one underroot is irrational number​

Answer 1

refer to attached Image ❤️

Answer 2

Step-by-step explanation:

Let us assume

2

1

is rational.

So we can write this number as

2

1

=

b

a

---- (1)

Here, a and b are two co-prime numbers and b is not equal to zero.

Simplify the equation (1) multiply by

2

both sides, we get

1=

b

a

2

Now, divide by b, we get

b=a

2

or

a

b

=

2

Here, a and b are integers so,

a

b

is a rational number,

so

2

should be a rational number.

But

2

is a irrational number, so it is contradictory.

Therefore,

2

1

is irrational number.