Question

prove that 5+underoot3 is an irrational number ​

Answer 1

Answer:

DEAR HUMAN BEING ,

Step-by-step explanation:

LET US ASSUME THAT 5 + √3 BE A RATIONAL NUMBER ,

THEREFORE , 5 + √3 = a\b , where , a and b are co-primes and b ≠ 0.

now ,

⇒√3 = a\b - 5

⇒√3 = a-5b\b

NOW , AS a-5b\b IS A RATIONAL NUMBER , SO , √3 SHOULD ALSO BE A RATIONAL NUMBER.

⇒BUT THIS CONTRADICTS THE FACT THAT √3 IS AN IRRATIONAL NUMBER.

⇒THUS , OUR ASSUMPTION WAS WRONG

⇒5 + √3 IS AN IRRATIONAL NUMBER