Question

prove that 6a√2+5÷3 is an irrational

Answer 1

Answer:

Step-by-step explanation

If possible let (6a√2+5) /3 be rational

So, (6a√2+5) /3 =p/q where p and q are coprimes and q not equal to 0.

6a√2+5 = 3p/q

6a√2= 3p/q - 5

√2= (3p/q - 5) /6a

Now on the RHS all are rational numbers.

3p/q - 5 will give a rational number because when two rational numbers are subtracted the result is always rational.

Then it is divided by 6a which again gives a rational number as the division of rational numbers also give rational numbers.

But √2 is an irrational number and a rational number cannot be equal to an irrational number.

So our assumption is wrong

Hence, (6a√2 + 5) /3 is irrational.