Question

3. Let x be a rational number and y be an irrational number. Is x+y
necessarily an irrational number? Give an example in support of
your
answer.
please solve you and please mark as me brainlist​

Answer 1

Answer:

The sum of any rational number and any irrational number will always be an irrational number. This allows us to quickly conclude that ½+√2 is irrational.

Answer 2

Answer:

Yes, it is necessary

Step-by-step explanation:

y is already an irrational number, it cannot be converted into a fraction

let's say sqrt5 or any square or sin4 or cos5 or sth like this (excluding the special cases for the trigonometric functions). They can't be converted into a fraction, even if you take its 10 digits, it would be inaccurate and the result is affected. sth like 0.6+sqrt2 is a definite irrational number since the sum of it can't be converted into a fraction after adding them together. Therefore x+y

is necessarily an irrational number.

Let's take x to be 4.5, y be sqrt20.

4.5+sqrt20

=8.972135955

this is only taken by 10 digits, there are more and they may not be recurring.(it wouldn't be anyway) like pi. pi has many digits, it can't be converted into a fraction no matter if it is added by any rational number so it is irrational. Therefore x+y is necessarily an irrational number.