Let x and y be rational and irrational numbers, respectively, then x + y necessarily an irrational number.

State True or False.

True

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False

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Solution

The correct option is A True
Yes.
Let x $= 21, y = \sqrt{2}$ be a rational number
Now $x + y = 21 + \sqrt{2} = 21 + 1.4142.... = 22.4142....$ , which is non-terminating and non-recurring. Hence x+y is irrational.

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Let x and y be rational and irrational numbers, respectively, then x + y necessarily an irrational number.State True or False.

The correct option is A TrueYes. Let x =21,y=√2 be a rational numberNow x+y=21+√2=21+1.4142....=22.4142.... , which is non-terminating and non-recurring. Hence x+y is irrational.

Let x and y be rational and irrational numbers, respectively, then x + y necessarily an irrational number.

State True or False.

The correct option is A True
Yes.
Let x $= 21, y = \sqrt{2}$ be a rational number
Now $x + y = 21 + \sqrt{2} = 21 + 1.4142.... = 22.4142....$ , which is non-terminating and non-recurring. Hence x+y is irrational.