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08 Jan 2018, 22:10
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Why cannot the square root of 4 be -2?
When x^2 = 4, then x can be + or -2. But when x = (4)^1/2, then x = 2 only... Why?
-2 * -2 = 4.
When x^2 = 4, then x can be + or -2. But when x = (4)^1/2, then x = 2 only... Why?
-2 * -2 = 4.
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08 Jan 2018, 23:10
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talismaaniac
\(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign (\(\sqrt{...}\)) always means non-negative square root.
The graph of the function f(x) = √x
Notice that it's defined for non-negative numbers and is producing non-negative results.
TO SUMMARIZE:
When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:
\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;
Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).
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08 Jan 2018, 23:34
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Bunuel
I think I do understand some of this. Much Thanks!!
