Question

Which of the following is a correct statement?
A. Sum of two irrational numbers is always irrational.
B. Sum of a rational and irrational number is always an irrational number
C. Square of an irrational number is always a rational number
D. Sum of two rational numbers can never be an integer.

Answer 1

Sum of a rational and irrational number is always an irrational number is a correct statement.

Option (A)  Sum of a rational and irrational number is always an irrational number is correct.  

 

Some useful results on irrational numbers :  

• The product of non zero rational numbers and an irrational number is an irrational number.
• The difference of rational numbers and an irrational number is an irrational number.
• The sum, difference, product and quotient of two irrational numbers need not  be an irrational number  

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Similar questions :

Which one of the following statements is true?

A. The sum of two irrational numbers is always an irrational number.

B. The sum of two irrational numbers is always a rational number.

C. The sum of two irrational numbers may be a rational number or an irrational number.

D. The sum of two irrational numbers is always an integer.

https://brainly.in/question/15896925#

 

Complete the following sentences:

(i) Every point on the number line corresponds to a ….number which many be either …… or ……

(ii) The decimal from of an irrational number is neither……. nor…..

(iii) The decimal representation of a rational number is either ……… or ……….

(iv) Every real number is either …………… number or ……………. number.

https://brainly.in/question/15896933

Answer 2

Step-by-step explanation:

__________❤HOLA❤_____

A. SUM OF TWO IRRATIONAL NUMBERS IS ALWAYS IRRATIONAL.✔✔

EXAMPLE :

$\sqrt{2} + \sqrt{3} = \sqrt{2} + \sqrt{3}$

B. SUM OF A RATIONAL AND IRRATIONAL IS ALWAYS AN IRRATIONAL NUMBER

EXAMPLE :

$3 + \sqrt{2} = 3 + \sqrt{2}$

C.SQUARE OF AN IRRATIONAL NUMBER IS ALWAYS A RATIONAL NUMBER

EXAMPLE :

${ \sqrt{2} }^{2} = 2$

D. SUM OF TWO RATIONAL NUMBERS CAN NEVER BE AN INTEGER