Question

Is (√2+√5)^2 is a rational number

Answer 1

yess....on expanding..
$2 \sqrt{10}$
remains....which is irrational

Answer 2

heya..

here is you answer..

$( \sqrt{2} + \sqrt{5} ) ^{2}$

$(a + b) ^{2} = {a}^{2} + {b}^{2} + 2(ab)$

${ \sqrt{2} }^{2} + { \sqrt{5} }^{2} + 2(2 \times 5)$

$2 + 5 + 2(10)$

$7 + 20$

$27$

$therefore \: { (\sqrt{2} + \sqrt{5} )}^{2} \: is \: a \: rational \: number.$

It may help you...☺☺