Question

if it is given that root 3 is irrational then prove that 17 - 15 root 3 is irrational​

Answer 1

Answer:

To the contrary, Let us that 17@15√3 is a rational number. Which means it can be written in the form of p/q where p and q are Co primes and q ≠ 0.

So,

17-15√3=p/q

-> 15√3=p/q -17

->√3= (p - 17) /q ×15

->√3 =p/15q -17

From above statement, we come to a conclusion that our RHS is a rational number and is equal to LHS but it is given that LHS is an irrational number which means out assumption was wrong.

Hence 17 - 15√3 is an irrational number.

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