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Two real numbers are defines as: ​ ​

a=0.444444444444...
b=0.354355435554... ​ ​

Determine whether each number is rational or irrational. Is the product of a and b rational or irrational? ​Justify your answers. ​Enter your answers and your justifications in the box provided.​

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A and B are irrational numbers. The product of a and b gives an irrational number.                                                                          

Step-by-step explanation:

Given:

a=0.444444444444...

b=0.354355435554... ​

To find:

rational or irrational

Solution:

  • A rational number is one that is in the form of a fraction. It will divide a/b and produces a remainder. Whereas an irrational number will be in the form of decimal format. The decimal goes unlimited.
  • Here a=0.444444444444... is an irrational number because it is in decimal form. B is also an irrational number. The product of a and b produces an irrational number.
  • So the answer is an irrational number.

                                                 

The two given real numbers are irrational numbers. The product of the two real numbers is a rational number.

What are rational and irrational numbers?

A rational number is a number that can be expressed as a fraction of two integers.

Examples of rational numbers are 1, 1/2 and 4.25

 

An irrational number is a number that cannot be expressed as the fractio of two integers.

To learn more about rational numbers, please check: https://brainly.com/question/20435423

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