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# Worked example: rational vs. irrational expressions (unknowns)

Sal determines whether expressions with unknown rational/irrational numbers are rational or irrational.

## Want to join the conversation?

• A question for the first problem, at

At , Sal says that the answer has to be rational, but this proves that it can be either rational OR irrational.

The numbers 5678 and 385 are rational.
So there's a and b, so a = ( m = 5678 and n = 2 )
b = ( p = 385 and q = 5)
5678 / 385 = 14.748051948051948 (which is Irrational isn't it?)

So the answer can be either Rational or Irrational, and not just rational right?
• Why do you think that the decimal is irrational? First, it is shown as a ratio of two integers which is rational by definition. Second, it starts repeating at the hundredths digit, and all repeating numbers are rational. I do not understand what you are trying to argue.
• if a and b are two rational numbers, e.g a= 22 and b= 7, then a/b = 22/7 which is pi, therefore will be an irrational number. so the answer @ should be irrational or rational. someone please explain!
• The important fact that you are missing is that 22/7 does not equal Pi. It is just an approximation for Pi. 22/7 = 3.142857.. where the 142857 repeats over and over again.
Pi is a non-ending and non-repeating decimal. Pi can not be written as the ratio of 2 integers.
22/7 is rational
Pi is irrational
Hope this helps.
• pie can be expressed in p/q where q doesnot equals to zero.Therefore it satisfies all conditions to be rational ,then why is it irrational?
• This is the same as your last question. The answer doesn't change. A rational number must be able to be written as the ratio of 2 integers. Pi can not be written as the ratio of 2 integers.
• Where can I get more practice of this?
• Repeat the exercises(practices) in the website after you've already completed them.
• Can the result of an irrational number plus or minus an irrational number be a rational number?
• Only if the two irrational numbers are the same, so √2 - √2 = 0.
• In what case can a number be both rational and irrational?
(1 vote)
• There is no such number. All real numbers are either rational OR irrational. They can't be both.
• Ok, according to the question at , what if we assume a=√4?
Then the problem would be: -25+√4 and √4 = 2.
Therefore it would be -25+2 i.e. -23. This answer is a rational.
So...shouldn't be the answer be "It can either be Rational or Irrational"??
(1 vote)
• Ah, but √4 is rational, so it wouldn't match the problem. It's asking for -24+a where 'a' is some irrational number. We would have to assume 'a' is irrational, so that takes out all the square root of perfect squares.
• pie=c/d.This seems to contradict the fact that pie is iirational.how will you resolve this contradiction?
HELP!
• To be a rational number, the number must be able to be written as the ratio of 2 integers.
You are assuming that circumference and diameter are both integers. They aren't. The circumference is irrational because it is defined using Pi: C = Pi*D