Question

Porove that 6+√2 is an
irrational number​

Answer 1

Step-by-step explanation:

Step-by-step explanation:

Let 6+root 2 is a rational number then we get that a and b two co-prime integers. Since a and b are two integers. Therefore (6-a/b)is a rational number and So root also is a rational number. But it is contradiction to fact root 2 =(6-a/b) is rational number.

Answer 2

To Prove :-

• 6 + √2 is a Irrational Number.

Proof :-

On the contrary let us assume that 6 + √2 is a rational number.

So it can be expressed in the form of p /q where p and q are integers and q is not equal to zero also HCF of p and q is 1.

Now as per our assumption ,

⇒ p/q = 6 + √2.

⇒ √2 = p/q - 6.

⇒ √2 = p - 6q / q .

N ow we cannot see that in LHS is a irrational number but in RHS as per our assumption p - 6q / q is a Rational number. This can never happen.

So we have arrived at a contradiction hence our assumption was wrong .

Hence 6 + √2 is a irrational number.