Question

Write a pair of irrational numbers whose sum is irrational.

Answer 1

Hint: Here, write two irrational numbers with the same sign, so that their sum remains an irrational number. If we add two same numbers with opposite signs the result will be 0, which is a rational number.

Complete step-by-step answer:
Rational Numbers:
The number of the form p/q where p and q are integers and q ≠ 0 are known as rational numbers. It is denoted by letter Q [Q comes from the word Quotient] and Rational comes from the word ‘Ratio’.
Example: 1/3, 4/5 etc.

IRRATIONAL NUMBERS:
The numbers which cannot be expressed in the form p/q where p and q are integers and q ≠ 0 are known as irrational numbers.
Example: Decimal representation is non-terminating and non-repeating ,√2, √3,1.010010001 etc.

We can write any pair of rational with same sign like \[\sqrt 2 + 2\sqrt 2 = 3\sqrt 2 \]
We can write any pair of irrational numbers. We will get an irrational number if two numbers do not cancel each other. As we know that the sum of irrational numbers can be both rational and irrational numbers, so carefully choose the pair of numbers.
So, the correct answer is “ \[\sqrt 2 + 2\sqrt 2 = 3\sqrt 2 \] ”.

Note: Properties of Irrational Numbers
1. Irrational number satisfies the commutative, associative and distributive laws for addition and multiplication.
2.(i) Sum of two irrational numbers need not be an irrational number.
(ii) Difference of two irrational numbers had to be an irrational number.
(iii) Product of two irrational numbers need not be an irrational number.
(iv) Quotient of two irrational numbers need not be an irrational number.