Question

prove that (1/2√13) is an irrational number. ​

Answer 1

Step-by-step explanation:

SOLUTION;

LET US ASSUME ,THAT (1/2√13) IS A RATIONAL NO.

THEN, (1/2√13) = P/ Q { P,Q ARE CO PRIMES ,AND Q IS NOT EQUALS TO. 0 }

= (1/2√13) = P/ Q

= √ 13 = 2P/Q

NOW , IF RHS ( 2P/Q) IS RATIONAL NO. ,THEN AS RHS = LHS ,RHS IS ALSO A RATIONAL NO. ,THIS CONTRADICTS THE FACT THAT WE KNOW AS √13 IS IRRATIONAL NO..

THIS CONTRADICTION HAS ARISED DUE TO OUR INCORRECT INITIAL ASSUMPTION THAT (1/2√13) IS RATIONAL NO.

SO ,HENCE PROVED THAT (1/2√13) IS A IRRATIONAL NO.

THANKS FRIEND, HOPE IT HELPS

Answer 2

The rational root theorem guarantees its roots aren't rational and since √13 is a root of the polynomial, it is irrational. Let √p=mn where m,n∈N. and m and n have no factors in common. So mn can not exist and the square root of any prime is irrational...

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