Question

Page 1.5
Sum of two irrational numbers is always:
a. an irrational number
b. a rational number
c. a non zero
d. none of these

Please Explain A Little

Answer 1

Hi there !!
Here's your answer

Sum of two irrational number is always :
d. None of these

Why ?

explaination :

The sum of two rational numbers can either be rational or irrational,
it depends upon the number chosen

Here are a few exceptions :

1. Lets say we have 2 irrational numbers:
( 2 + ✓5) and the other to be ( 2 - ✓5)

When we add this,
we get
2 + ✓5 + 2 - ✓5 in which -✓5 and ✓5 when added will become 0
and we're left with 2 + 2 = 4
here,
4 is a non zero RATIONAL number

2. Now ,in case a irrational number as the sum,
we take 2 numbers

✓5 and ✓2
✓5 = 2.23606...
✓2 = 1.41421...
when we add 2 numbers,
we get 3.65207... which is non terminating and non recurring .

Also,
✓5 and -✓5 are 2 irrational numbers whose sum is 0 ,ie, a rational number.

Hence,
the option is d. None of this



Hope you got it cleared !!

Answer 2

The sum of two irrational numbers is SOMETIMES irrational." The sum of two irrational numbers, in some cases, will be irrational. However, if theirrational parts of the numbers have a zero sum (cancel each other out), thesum will be rational.
.
.
.
hope it may help you