Are there two irrational numbers whose sum and product both are rationals? Justify.

Solution:

Let us consider two irrational numbers 3 + √2 and 3 - √2

We know that

Sum of two irrational numbers = 3 + √2 + 3 - √2

= 6

Here 6 is a rational number

Product of two irrational numbers = (3 + √2) (3 - √2)

= 9 - 3√2 + 3√2 - 2

= 7

Therefore, there are two irrational numbers whose sum and product both are rationals.

✦ Try This: The value of (√26 + √49)/(√8 + √5) is equal to

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

NCERT Exemplar Class 9 Maths Exercise 1.2 Sample Problem 1

Are there two irrational numbers whose sum and product both are rationals? Justify

Summary:

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. Yes, there are two irrational numbers whose sum and product both are rationals

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