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May 9, 2015 · Because a an irrational number times a rational number is irrational, we have an irrational number equaling a rational number which is a contradiction. My question is: Is this …
Jun 3, 2015 · Here is a very simple general proof that the square root of any integer that is not a perfect square is irrational. For convenience, write a|b a | b (read 'a divides b') for 'b is …
Oct 17, 2017 · You should have in your tool box the proof that $\sqrt 2$ is irrational. And it is pretty easy to generalize that proof to show that the square root of a non-perfect square is irrational. …
Apr 9, 2015 · Eg: calculate $1.5^2$. If this is < 3, try $1.6^2$, $1.7^2$ until we find a value which squares to more than 3. Then do the same with the next digit: try 1.75 and see whether to go …
Trivially, a rational number has a rational square root if and only if it's the square of some rational number. As the other answers note, various other characterizations can be given, e.g. that …
Then its square is rational, because multiplying rationals gives a rational. But $ (\sqrt 2 + \sqrt 3)^2=2+2\sqrt 6 +3$ is irrational because the sum of an irrational and a rational ($5$) is …
The number $\sqrt {3}$ is irrational ,it cannot be expressed as a ratio of integers a and b. To prove that this statement is true, let us Assume that it is rational and then prove it isn't …
However, it is straightforward to check that none of $\pm 1, \pm 3$ are solutions to $x^2-3=0$. Therefore there are no such rational solutions and $\sqrt {3}$ is irrational.
Aug 25, 2015 · There is a similar question however that question asks why $3 |p^2$. Here the question is about $ 3 | p^2 \\rightarrow 3 | p$. It is a simple exercise (1.2.1) from Abbot's …
Jan 30, 2017 · Closed 3 years ago. Is my proof that the square root of a positive integer is either an integer or an irrational number correct? The proof goes like this: Suppose an arbitrary …
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