Question

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

Answer 1

SOLUTION :  

This statement the sum of two irrational number is an irrational number is FALSE.  

Because if we add two irrational numbers, we may get an irrational number or a rational number.

For e.g :  

★★Let two irrational numbers be  

a = 1 + √2  &  b = 1 - √2

a + b = 1 + √2 + 1 - √2

a + b = 1 + 1 + √2 -√2

a + b = 2 +0= 2

a + b = 2 [RATIONAL]

★★Let two irrational numbers be  

a = √2 +1  &  b = √2 - 1

a + b = √2 + 1 + √2 - 1

a + b = √2 + √2 + 1 - 1

a + b = 2√2 +0 = 2√2 [IRRATIONAL]

Hence, the sum of two irrational number is an irrational number is  FALSE.  

★★★RATIONAL NUMBERS : A number that can be expressed in the form p/q,  where p and q are integers and q ≠ 0 is called rational number.

★★★ IRRATIONAL NUMBERS :  

A number that cannot be expressed in the form p/q,  where p and q are integers and q ≠ 0 is called irrational number.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hi !!

Sum of two irrational number is sometimes rational number or irrational number...

Ex :- let two irrational be √3 - 1 and √3 + 1.

Sum of √3 - 1 and √3 + 1 = √3 - 1 + √3 + 1 = 2√3 [ Which is irrational number ]

Or,

Let two irrational numbers are 1 - √3 and 1 + √3.

Sum = 1 - √3 + 1 + √3 = 2 [ Which is rational number ]

So, the given statement is false.

Hope it will help you!!