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Assume it's rational. Then 2 + root2 = some rational number q. Then root2 = q - 2. However, the rational numbers are well-defined under addition by (a,b) + (c,d) = (ad + bc, bd) (in other words, you can add two fractions a/b and c/d and always get another fraction of the form (ad + bc)/bd.) Therefore, q - 2 = q + (-2) is rational, since both q and -2 are rational. This implies root2 must be rational, which is a contradiction. Therefore the assumption that 2 + root2 is rational must be false.
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Is there a proof to show that if you multiply an irrational number times an irrational number you get a rational number?
There cannot be a proof since your assertion is not necessarily true. sqrt(2)*sqrt(3) = sqrt(6). All three are irrational numbers.
How can the pythagorean spiral be used to show the exact value of an irrational number?
It cannot. It can only show square roots which represent only a small proportion of irrational numbers.
How do you show your work for the square root of 32 round to the nearest hundredths?
It is an irrational number and rounds to 5.66 to the nearest hundredths
How to prove that Assuming 5 is irrational how would you prove that 5 is irrational?
Root signs didn't show up
If you take the square root of an irrational number.Will it be irrational too?
Certainly. Otherwise, there would be a rational number whose square was an irrational number; that is not possible. To show this, let p/q be any rational number, where p and q are integers. Then, the square of p/q is (p^2)/(q^2). Since p^2 and q^2 must both be integers, their quotient is, by definition, a rational number. Thus, the square of every rational number is itself rational.
Who was the first person to show that two is an irrational number?
No one has ever shown that 2 is an irrational number because it is rational.
Is there a proof to show that if you multiply an irrational number times an irrational number you get a rational number?
There cannot be a proof since your assertion is not necessarily true. sqrt(2)*sqrt(3) = sqrt(6). All three are irrational numbers.
How can the pythagorean spiral be used to show the exact value of an irrational number?
It cannot. It can only show square roots which represent only a small proportion of irrational numbers.
Is the set of irrational numbers closed under subtraction?
No; here's a counterexample to show that the set of irrational numbers is NOT closed under subtraction: pi - pi = 0. pi is an irrational number. If you subtract it from itself, you get zero, which is a rational number. Closure would require that the difference(answer) be an irrational number as well, which it isn't. Therefore the set of irrational numbers is NOT closed under subtraction.
Is the product of three irrational numbers always an irrational number?
No. The easiest counter-example to show that the product of two irrational numbers can be a rational number is that the product of √2 and √2 is 2. Likewise, the cube root of 2 is also an irrational number, but the product of 3√2, 3√2 and 3√2 is 2.
Is decimal 1111 a rational or irrational number show your work?
.1111 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Pi is an irrational number. How do you show pi on the number line?
It is very had to show that but you could approximate it with 22/7. (or just round it to 3.14159265) 22/7=3.142857142857... pi=3.14159265...
How do you express irrational number on a number line?
Simply plot the irrational number at it's approximate location on the number line and label the irrational number. For example, if you were to plot pi on the number line, you would plot it at about 3.14 and label it with "π" (the pi symbol, if it doesn't show up) Another example is if you want to plot the square root of 2 on the number line. You would plot it at around 1.414 and label it with "√2"
Is 0 a rational number or an irrational number?
zero technically isn't a number. it represents the absence of a number. It's nothing, and it's just used to show when there isn't any number
How do you show your work for the square root of 32 round to the nearest hundredths?
It is an irrational number and rounds to 5.66 to the nearest hundredths
How do you show that there are irrational numbers between every rational number?
"Every rational number" is a single value and there cannot be anything between only one thing!
How to prove that Assuming 5 is irrational how would you prove that 5 is irrational?
Root signs didn't show up
