Question

prove that
$\sqrt{2 \: \ \: + \sqrt{3 } }$
root 2+root 5 is an irrational number
​

Answer 1

Answer:

Step-by-step explanation:

DEAR HUMAN BEING,

LET US ASSUME THAT ROOT(2 + ROOT 3) BE RATIONAL NUMBER.

I.E  ROOT(2 + ROOT 3) = A\B , WHERE , "A" AND "B" ARE CO PRIMES AND B

                                         NOT EQUAL TO 0.

= 2 + ROOT 3 = A^2\B^2               (SQUARING BOTH SIDES)

= ROOT 3 = A^2\B^2 - 2

= ROOT 3 = A^2-2B^2\B^2.

AS ON L.H.S , THE NUMBER IS RATIONAL , THUS , ROOT 3 SHOULD ALSO BE RATIONAL NUMBER.

=BUT THIS CONTRADICTS THE FACT THAT ROOT 3 IS AN IRRATIONAL NUMBER.

= THUS , OUR ASSUMPTION WAS WRONG..

= ROOT(2+ ROOT 3) IS AN IRRATIONAL NUMBER.

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