Question

prove that √p+√q is a irrational​

Answer 1

Answer:

Let p and q be the irrational numbers

Therefore the roots of the irrational numbers will also be irrational..

i.e.√p+√q= irrational....

Thank you ☺✌..

Answer 2

Step-by-step explanation:

TO PROVE THAT ROOT P PLUS ROOT Q IS A RATIONAL NUMBER .

LET ROOT P PLUS ROOT Q IS A RATIONAL NUMBER IN THE FORM OF x by y.

$\sqrt{p} + \sqrt{q} = \frac{x}{y}$

squaring both sides

${ (\sqrt{p} + \sqrt{q}) }^{2} = \frac{ {x}^{2} }{ {y}^{2} }$

$p + q + 2 \sqrt{pq} = \frac{ {x}^{2} }{ {y}^{2} }$

$\sqrt{pq} = \frac{1}{2}( \frac{ {x}^{2} }{ {y}^{2} - p - q) }$

NOW, P AND Q ARE PRIME POSITIVE NUMBERS HENCE HERE CONTRADICTION ARISES AND HENCE PROVED.