Question

Give examples for sum of two irrationals
to be (a) irrational (b) not an
irrational.​

Answer 1

$\huge{\underline{\underline{\sf{\pink{Answer:-}}}}}$

sum of two irrationals can be rational or irrational

Example for sum of two irrationals being irrational,

$\sqrt{2} \: \: is \: \: irrational$

now,

$\sqrt{2} + \sqrt{2} = 2 \sqrt{2}$, which is irrational again.

Example for sum of two irrationals being rational:

$√2\:and\:1−√2$are irrational.(Note that$1−√2$is irrational from the second statement.) But,$√2+(1−√2)=1$which is rational.

so, the sum of two irrationals can be both rational and irrational