Question

show that root 17 is irrational ​

Answer 1

let us assume root 17 is a rational number.

if it is rational then there must be exist two integers x and y (y=/0).such that

$\sqrt{17} = x \div y$

if x and y have a common factor other than 1.then,we divide by common factor get

$\sqrt{17} = a \div b$

where a and b are co primes.

in squaring both sides we get 2b^=a^

so we can write a =2c

2v^=4c^ that is b^=2b^

therefore both and b as common factor but this contradicts the fact the a and b are co prime s

this contradiction has arisen because of our assumption that

$\sqrt{17}$

is rational.this assumption is false .

so we conclude that

$\sqrt{17}$

is irrational.