Question

prove that root 3- root 5 is an irrational number​

Answer 1

$\huge{\underline{\underline{\bf{\purple{answer}}}}}$

$let \: \sqrt{3} - \sqrt{5} \: \: be \: \: rational$

$\sqrt{3} - \sqrt{5} = \frac{p}{q}$

{ p and q are integer and co-prime, q is not equal to 0 }

$\sqrt{3} = \frac{p + \sqrt{5} }{q}$

Since we know that root 3 is irrational

So , Our assumption is wrong.

Hence root 3 - root 5 is irrational.

Answer 2

Step-by-step explanation:

let

3

−

5

berational

\sqrt{3} - \sqrt{5} = \frac{p}{q}

3

−

5

=

q

p

{ p and q are integer and co-prime, q is not equal to 0 }

\sqrt{3} = \frac{p + \sqrt{5} }{q}

3

=

q

p+

5

Since we know that root 3 is irrational

So , Our assumption is wrong.

Hence root 3 - root 5 is irrational