Question

proove that 6+√2 is an irrational number​

Answer 1

let us assume to the contrary that 6+root 2 is rational and 6+root2 is equal to a/b where a and b are co-primes

so, 6+root2=a/b

root2=a/b-6

root2=a-6b/b

now, root 2 becomes rational , but this contradicts the fact that root 2 is irrational.

Thus , our assumption that 6+root2 is rational was wrong.

Hence 6+root2 is rational.

hope it helped ^_^

Answer 2

Answer:

Step-by-step explanation:

Let us assume that 6+ root2 is rational.

Then, it can be written in the form a/b, where a and b are co-prime numbers, as it is a rational number.

=> 6+ root2 = a/b

=> root2 = a/b -6 = (a-6b)/b [Taking b as LCM]

But, we know that root2 is irrational.

Therefore, our assumption is wrong.

Hence, 6+ roo2 is also irrational.

Proved...