Question

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

Answer 1

Once again we proceed by successive magnification, and successively decrease the lengths of the portions of the number line in which 5.37 bar is located. First, we see that 5.37 bar is located between 5 and 6. In the next step, we locate 5.37 bar between 5.3 and 5.4. To get a more accurate visualization of the representation, we divide this portion of the number line into lo equal parts and use a magnifying glass to visualize that 5.37 bar lies between 5.37 and  5.38. To visualize 5.37 bar more accurately, we again divide the portion between 5.37 and 5.38 into ten equal parts and use a magnifying glass to visualize that S.S lies between 5.377 and 5.378. Now to visualize 5.37 bar still more accurately, we divide the portion between 5.377 and 5.378 into 10 equal parts, and visualize the representation of 5.37 bar as in fig.,(iv) Notice that 5.37 bar is located closer to 5.3778 than to 5.3777(iv)