How do you compare square roots? Of course, the positive square root of 49 is greater than the positive square root of 36. However, what if you were to have $\pm\sqrt{49}$ ? $\pm\sqrt{36}$? Would it be $\gt$, $\lt$, or some other symbol. Also, what if you had $\pm\sqrt{16}$ ? 0?
2026-04-29 20:53:03.1777495983
Comparing Square Roots
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You can only compare two real numbers. $\pm \sqrt{x}$ may be interpreted as the unordered pair $\{\sqrt{x},-\sqrt{x}\}$, so it is usually meaningless to compare it with something else, in the same way that it is meaningless to compare $\{1,3\}$ and $2$ or $\{1,4\}$ and $\{2,3\}$. What you can say is $1 < 2 < 3 < 4$.