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### Course: Algebra 1>Unit 15

Lesson 2: Sums and products of rational and irrational numbers

# Sums and products of irrational numbers

The sum of two irrational numbers can be rational and it can be irrational. It depends on which irrational numbers we're talking about exactly. The same goes for products for two irrational numbers. This video covers this fact with various examples.

## Want to join the conversation?

• at 4.50 Sal says that pi squared is irrational .how do we know that?
• Is it always the case that when we multiply two irrational numbers, the product will be EITHER an irrational number OR an integer? I am asking because I have yet to see an example where the product of two irrational numbers yields a rational non-integer.
• This is not always the case. A counter example would be √1.125 * √2 = 1.5
• at , could someone please explain why 1/π is irrational, because isn't it just the ratio of two numbers?
• Rational numbers must be the ratio of 2 integers. Pi is not an integer. It is an irrational number. 1/Pi is also an irrational number.
• how is pi+1-pi= 1 because those numbers are both irrationals. Also if pi+pi=2 pi
then what difference does it make to pi being subtracted by 1, pi has an infinite amount of numbers so you cant subtract it by 1. Even if you can wouldn't the number replace itself or something because the numbers pi have are INFINITE!!. I also want to confirm this method to so that i don't have anything else to say,let me assume that a very dumb person; ahmm (myself), assumed that if pi + pi = 2 pi but there is a minus 1 there so i can subtract 2 by 1 it would still make it pi? please dont make fun of my stupidity im only 11 so if you can pleas answer my question i will be very grateful
• pi + 1 - pi addition is commutable, so you can move things around as long as you keep the sign, so pi - pi + 1 is the same, and anything minus itself (even irrational numbers) is always 0, so all that is left is 1 = 1
If pi is 3.14159..., so if you subtract 1, you would have 2.14159..., but as you expected it does not mean much.
• can't you just write an irrational number and divide it by 1 then call it rational number?
• I guess I've found the answer:

"a rational number is one that can be expressed as the ratio of two integers, and an irrational number is not an integer."
• can you please teach me the sum of rational numbers
• No.
But fine:
By definition, a rational number can be expressed as a fraction with integer values in the numerator and denominator (denominator not zero). So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number.

statementbox "The sum of two irrational numbers is SOMETIMES irrational."

Product of a two rational numbers is rational
• i dont understand how pi + (1-pi) is rational? or sqrt of 2 x sqrt of 2 is 2? when i do it in my calculator it doesnt come out that way
(1 vote)
• pi-1+pi = 1 (a rational number) because Pi-Pi=0
sqrt(2)*sqrt(2) = sqrt(4) = 2 because 2^2 = 4
• so this is all for 7th graders to get ready for 8th grade
• an irrational number is a number or pi that is with the addition, subtraction, multiplication, or division of math
(1 vote)
• At , he says pi-pi=c when he plugged it in for a and b, but wouldn't it be a + a then because he is using the same number for different variables?