Is the "Square Root of 4" equal to ±2 or 2? And the twist here is that if it is equal to ±2, then, what is "√4 + 2"? Is "√4 + 2" equal to just "4", or "4 and 0"? I am studying root right now and I just cant figure it out.
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The convention is that if $x>0$ then $\sqrt x >0$. – DanielWainfleet Sep 04 '17 at 08:07
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The square root of $a$, $\sqrt{a}$ where $a\geq 0$ is defined as the unique, nonnegative number which yields $\sqrt{a}\cdot\sqrt{a}=a$. The same goes for the $n$-th root of $a$.
If instead you are looking at a quadratic equation $x^2=4$, you are interested in all solutions to this equation. Here you get that not only $\sqrt{4}=2$ is a solution but also $-\sqrt{4}=-2$.
Hirshy
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But
x^2 = 4can be rewritten to bex = square root of 4. Then, it will no longer be a quadratic equation. What answer will this yield? – WhatsYourIdea Sep 04 '17 at 06:46 -
No, it can't be rewritten as just $x=\sqrt{4}$. Why should that be the case? – Hirshy Sep 04 '17 at 06:48
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Those expressions arent equivalent, since square root is defined to be positive, @WhatsYourIdea – Abdullah al allah Sep 04 '17 at 06:49
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@DavidMitra you are absolutely right, I was going for $a>0$ first and then changed my mind. I will edit that as soon as I get back to a computer. – Hirshy Sep 04 '17 at 07:10
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Both $2$ and $-2$ are square roots of $4$, but the principal square root, represented by $\sqrt{4}$, is $2$. – A.Γ. Sep 04 '17 at 07:22