Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an irrational number? Give an example in support of your answer

Solution:

We know that

Sum of a rational and an irrational number is irrational.

If x is a rational number and y is an irrational number, the sum x + y is irrational

Example -

Consider x = 5 and y = √3

So the sum

x + y = 5 + √3

which is irrational.

Therefore, the statement is true.

✦ Try This: The value of (√18 + √60)/(√10 + √5) is equal to

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1

NCERT Exemplar Class 9 Maths Exercise 1.2 Problem 1

Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an irrational number? Give an example in support of your answer

Summary:

The statement “Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an irrational number” is true

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