







The square root of 6 is irrational 
20171002 

From John: http://mathcentral.uregina.ca/QQ/database/QQ.09.06/sylvia1.html
In the initial assumption of that proof, root 6 is assumed to be a/b where a and b have no common factors, but why does having a common factor make it irrational? Answered by Penny Nom. 





Is the square root of 2 plus the square root of 2 irrational? 
20170329 

From haya: how can i prove the the square root of 2 plus the square root of 2 is an irrational number? Answered by Penny Nom. 





An example of an irrational number 
20151022 

From Allison: It ask me to find an example of an irrational number less than 5 and I don't
understand what the difference from a rational number and an irrational
number besides the fact that a rational number can be repeated and shown in
a simple fraction and an irrational number can't be written in a simple
fraction.
Can you help me? Answered by Penny Nom. 





2.236... 
20151013 

From Ann: 2.236...
What is the most specific category of numbers does this fall into? Rational or Irrational? Does the .... mean that it repeats? Answered by Harley Weston. 





Square roots 
20150921 

From mariana: I have read various articles on how to find the square root of irrational numbers and every article out there seems to be very confusing.
i read you answer to LUKOW about irrational numbers and i am still quite confused. Say i want to find the square root of 326. i know that it is between 18 and 19 because 18 is the square root of 324 and 19 is the square root of 361 im just very confused about the rest of the process. Please help! ( if possible i would appreciate two examples. thanks) Answered by Penny Nom. 





Is 22/7 is an irrational number? 
20150607 

From Sayak: Is 22/7 is an irrational number Answered by Penny Nom. 





1.2731568 
20100616 

From angel: is 1.2731568 a natural number a whole number a irrational number or a inter Answered by Robert Dawson. 





Proof that the root of 27 is irrational 
20091018 

From Scarlet: How do you prove that the square root of 27 is irrational? Answered by Victoria West. 





root 2 is irrational 
20090731 

From prateet: prove that root2 is an irrational number. Answered by Robert Dawson. 





Nonterminating, nonrepeating decimals 
20080803 

From Peter: How do you take a random, nonterminating, nonrepeating decimal into a fraction? Answered by Stephen La Rocque. 





How can the distance between two points be irrational? 
20080507 

From Dawn: Yesterday my advanced 7th grade prealgebra students were finding the distance between two points on a coordinate grid using the distance formula. A student asked me how come we or math I guess is able to represent a finite distance with an irrational number. I found this to be a very interesting question. I and the 7 other math teachers on my staff had discussed this and we have a variety of thing to say to the kid, but nothing that amounts to an actual answer. The students have studied what it means for a number to be irrational, and they cannot understand how that can "measure" a line that obviously stops. Got any suggestions? Answered by Stephen La Rocque, Penny Nom, Claude Tardif and Victoria West. 





Is this an irrational number? 
20080322 

From Tom: Is it possible to build an irrational number with numbers that are just 1's and 2's where only finitely many 2's appear? If so, how do we build it and how do we know it is irrational? Answered by Penny Nom. 





An irrational number 
20071029 

From Clara: Find an irrational number between 0.53 (with 53 as repeating)
and 0.54 (with 54 repeating)
I changed each to 53/99 and 54/99 with 1/99 being the difference.
Please help me. Answered by Stephen La Rocque, Penny Nom and Harley Weston. 





Irrational functions 
20071001 

From alicia: i have a question about irrationals functions.
i have been using them quite some time now, but i wonder where they can be found in daily life?
i hope you can help me, Answered by Harley Weston. 





The irrationality of PI 
20070807 

From Matthew: I have what I like to think of as a rather interesting question that I can't explain confidently for the life of me.
If we take a circle with a radius of 1 and we calculate the circumference, we can use 2 pi R.
Doing this calculation results in a circumference of 6.28318530717~ which goes on forever.
However, if you were to take a that same circle in the real world, say with radius 1cm and wrap a string around
it, and then measure the string, you don't get 6.28~, you get something like 6.2, a much more finite distance. The length
of the string is not an irrational number, like the math claims it to be. Answered by Claude Tardiff and Stephen La Rocque. 





Prove that square root of 3 is irrational. 
20061221 

From Humera: Prove that square root of 3 is irrational. Answered by Stephen La Rocque. 





Help me prove that the square root of 6 is irrational 
20060923 

From Sylvia: Could you please help me prove that the square root of 6 is irrational ? Answered by Stephen La Rocque. 





The square root of 2 
20020305 

From Roger: Does two (2) have a square root or do the numbers just keep going? Are there any other numbers that behave like two when it comes to extracting the square root? Answered by Penny Nom. 





Some irrational numbers 
20010703 

From Kellie:
 Is it possible to write pi as a fraction?
 Is it possible to write the square root of 2 as a fraction.. Explain why?
Answered by Harley Weston. 





Cube roots on a calculator 
20010324 

From Will: Hi my name is Will.I have a question about the calculator TI83 Plus or the use of a scientific calculator. It is about using them to turn a cubed root to a decimal. When using that for a rational and irrational number. Rational numbers is a number that terminates or repeates. A irrational number goes on and on and uses ... (like pie). Like when you type the cube root of 8 it gives you 2, and that is a rational number. The squre root of 2 is 1.41421356... that is irrational. So why is it when you put the cube root of 16 in the calculator it says 2.5198421 that is rational it terminates at the ninth digit and my float is set for the tenth? But why when you do it by hand you get the 2 times the cube root of 2 and that is irrational? Why is that? Answered by Judi McDonald. 





The nth place of pi 
20010227 

From Andrew: I have always wondered; is it possible to find the value of an irrational number, such as (phi) at it's nth decimal place??? You would plug the decimal place into the formula and the value would be given at the specified decimal place. When we look at the expression { (sqr 5 + 1)/2 } we are in a sense visualising the number in it's entirety, so the formula may include elements of the above expression in some form. Answered by Claude Tardif. 





Rational Numbers 
20000914 

From Josh Kuhar: How can you tell a number is rational? Answered by Harley Weston. 





The square root of 3 
20000404 

From Mr. William: Prove that root 3 is irrational Answered by Harley Weston. 





Rationals, irrationals and integers 
20000314 

From Erin McKeon: Why does the letter J represent the set of integers, the letter Q represent a set of rational numbers and the letter P represent a set of irrational numbers? What do each of these letters stand for? Answered by Harley Weston. 





Pi 
20000222 

From Shelley Collier: Numbers that can be written in the form p/q where p and q are integers, (q not 0), are known as rational numbers. What you are missing is that p and q must be integers. The fact that Pi is irrational means that you can't have a circle with both the circumference and diameter being integers. In fact you can't even have the circumference and diameter both rational since the quotient of two rationals is again a rational. Answered by Claude Tardif and Penny Nom. 





Irrational algebraic functions 
20000221 

From Bucky Cadena: Here is the multipart problem: Given f(x) = x3* squareroot of x + 4 What does the f(x) intercept equal Find the two values for which f(x) = 5 Find the one value for which f(x) = 3 Answered by Harley Weston. 





The square root of two is never supposed to end 
19990306 

From a wondering student: i am algebra II and am in the 9th grade. today we were talking about rational and irrational numbers. When we were talking about square roots my friend and i were talking and we thought of something. if you have a square with sides of length one then the diagonal of the square is the square root of 2. Now the square root of two is never supposed to end. But the diagonal of the square ends so therefore doesn't the square root of 2 end. our math teacher did not really answer our question because it was not in the lesson plan and not to many people would see where we were coming from. the answer is really bugging me and i would like to have your input. Answered by Jack LeSage and Penny Nom. 





Root 17 is Irrational 
19990121 

From John Murdock: If you could help me out with this I would appreciate it. Prove that the square root of 17 is irrational. Answered by Harley Weston. 





6.99999... = ? 
19981205 

From Tom: I have had a rather heated arguement with my students. Please settle this for me. Solve <,>, = 6.99999... __ 7 Thank you. Answered by Penny Nom. 





Terminating decimals 
19981116 

From Debra Karr: A college student studying elementary education asked me a question that I could not think of the correct answer. How can you look at a fraction and tell if is a terminating or non terminating decimal? Answered by Jack LeSage and Penny Nom. 





Rational and Irrational Numbers 
19980919 

From Ri: I am trying to explain rational & irrational numbers to my niece who is grade 7 and am having difficulties. Could you please explain the difference between rational & irrational numbers. Thank you Ri Answered by Penny Nom. 





Rational Numbers 
19980905 

From Kristin Mckenzie: Iam a secondary student with a math question I don't know how to do. This is the question: Explain whether each decimal number represents a rational number. (a) 0.16 (b) 0.12 (c) 3.125 (d) 0.27 (e) 0,212 112 111 2 .... (f) 0. 457 92 If it wouldn't be a problem i would really appreciate it if you sent back the instructions on how to do the question. My name is Kristin Mckenzie and my return email is lexus1999@hotmail.com Thankyou for you time Answered by Jack LeSage and Harley Weston. 





A proof that e is Irrational. 
19970430 

From Peter Hall and Jenny: We have a little mathematical problem... we need some help proving e is an irrational number! We don't feel very confident in our formulas, so if You have the time to give us a little explanation we would be very grateful!!! Answered by Doug Farenick and Penny Nom. 





Repeating Decimals 
19970124 

From Grant Reed: Is there a way to tell that the repeating decimal for 1/17 has no more than 16 repeating digits? Answered by Penny Nom. 





Ses points de discontinuités est les irrationnelles 
20020108 

From Un eleve: Je voudrait montrer qu'il n'existe pas de fonction de R>R tels que ses points de discontinuités est les irrationnelles, en utilisant la methode de "baire". Answered by Claude Tardif. 

