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Is the number 2 Irrational?
Are irrational numbers always rational?
What are irrational numbers?
Is the square root of 2 Irrational?
In this proof we want to show that √2 is irrational so we assume the opposite, that it is rational, which means we can write √2 = a/b. Now we know from the discussion above that any rational number that is not in co-prime form can be reduced to co-prime form, right?
- Irrational numbers: FAQ (article)
For example, 2 + 18 = 4 2 , which is another irrational...
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And then if you just take that irrational number and you...
- Irrational numbers: FAQ (article)
- The Square Root of 2
- Irrational
- Reductio Ad Absurdum
- History
- Conclusion
Is the square rootof 2 a fraction? Let us assumethat it is, and see what happens. If it is a fraction, then we must be able to write it down as a simplifiedfraction like this: m/n (m and n are both whole numbers) And we are hoping that when we square it we get 2: (m/n)2= 2 which is the same as m2/n2= 2 or put another way, m2 is twice as big as n2: ...
We call such numbers "irrational", not because they are crazy but because they cannot be written as a ratio(or fraction). And we say: "The square root of 2 is irrational" It is thought to be the first irrational number ever discovered. But there are lots more.
By the way, the method we used to prove this (by first making an assumption and then seeing if it works out nicely) is called "proof by contradiction" or "reductio ad absurdum".
Many years ago (around 500 BC) Greek mathematicians like Pythagoras believed that all numbers could be shown as fractions. And they thought the number line was made up entirely of fractions, because for any two fractions we can always find a fraction in between them (so we can look closer and closer at the number line and find more and more fractio...
The square root of 2 is "irrational" (cannot be written as a fraction) ... because if it could be written as a fraction then we would have the absurdcase that the fraction would have even numbers at both top and bottom and so could always be simplified.
Euclid proved that √2 (the square root of 2) is an irrational number. He used a proof by contradiction. First Euclid assumed √2 was a rational number. A rational number is a number that can be in the form p/q where p and q are integers and q is not zero.
The number √ 2 is irrational. In mathematics, the irrational numbers ( in- + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.
The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself or squared, equals the number 2. It may be written in mathematics as or . It is an algebraic number, and therefore not a transcendental number.
