# The Sum of Two Irrational Number is an Irrational Number (True/False). - Mathematics

Match the Columns
True or False

The sum of two irrational number is an irrational number (True/False).

#### Solution

The sum of two irrational numbers is an irrational number (True/False)

False

Reason:
However, sqrt2
is not rational because there is no fraction, no ratio of integers that will equal sqrt2
. It calculates to be a decimal that never repeats and never ends. The same can be said for  sqrt3. Also, there is no way to write sqrt2+sqrt3 as a fraction. In fact, the representation is already in its simplest form.

To get two irrational numbers to add up to a rational number, you need to add irrational numbers such as  1+sqrt3 and 1-sqrt2. In this case, the irrational portions just happen to cancel out leaving: 1+sqrt2+1-sqrt2=2 which is a rational number (i.e. 2/1).

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 1 Real Numbers
Q 28 | Page 58