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root of negative number?

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yamini
 Post subject: root of negative number?
 Post Posted: Wed Oct 24, 2007 3:13 pm 
some where I read root of negative number is undefined.

According to the OG10, cube root of -89 is between -4 and -5.

In this case what is sqrt(-4) ?
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StaceyKoprince
 Post subject:
 Post Posted: Thu Oct 25, 2007 5:01 pm 
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ManhattanGMAT Staff


Posts: 5783
Location: San Francisco
You will not see a square root sign with a negative number underneath it on the test - this is an example of an imaginary number and imaginary numbers are not tested on the GMAT. (This does not mean that you won't see something like x^2 = 16 and you have to solve that as +4 and -4. But notice that what I just typed in the previous sentence does not include a square root sign.)

A cube maintains the sign of the original number. A square does not; instead, a square is always positive. So you can take the cube root of a negative number, but not the square root of a negative number because, by definition, a square of a real number is always positive.

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