Question

Prove that 13√5/7 is an irrational number

Answer 1

HEY MATE !!!

$let \: \frac{13 \sqrt{5} }{7} \\ \: be \: rational$

thus it can be expressed in the form of

$\frac{p}{q}$

where p and q are integers and q not equal to 0

thus,

$\frac{13 \sqrt{5} }{7} = \frac{p}{q} \\ \\ 13 \sqrt{5} = \frac{7p}{q} \\ \\ \sqrt{5} = \frac{7p}{13q}$

Irrational = Rational

since this can not be true

this contradiction has arised due to the wrong assumption thus, 13√5 / 7 is irrational

HENCE PROVED

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Answer 2

let us think that it is rational no.

so it will be in the form of p/q, where q is not equal to 0 n q n p are co primes

so we can write it

p/q=13 \sqrt{5} \7

taking 7 n 13 on LHS we are left with root 5

the p/q×7/13 is a rational no. so root 5 will also be rational

but root 5 is an irrational . so our assumption was wrong that 13root5/7 is rational .

so it is irrational.

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