Question

how to prove 2+3root2 divided by 7 is irraational

Answer 1

Answer:

We have to prove 2 + 3√2 / 7 is an irrational

Step-by-step explanation:

Proof by contradiction:

If possible , then let us assume 2 + 3√2 / 7 be a rational number.

Thus, (2 + 3√2 / 7) - (2 / 7) = 3√2 / 7 is a rational number (Since difference of two rational numbers is a rational number)

Also,

( 3√2 / 7 x 1 / 3) = √2 / 7 is also a rational number. (Since product  of two rational number gives a rational number )

Also, again √2 / 7 x 7 / 1 = √2 is also a rational number  (Since product  of two rational number gives a rational number )

But this contradicts the fact that √2 is irrational .

This contradictionarrises by assuming that 2 + 3√2 / 7 is a rational number.

Thus, our assumption was wrong, 2 + 3√2 / 7 is an irrational number.

Hence proved.....