Aren't both 5 and -5 the square roots of 25?

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Meg

2017. május 27. 1:25

I was doing a problem that resulted in two possible values for the variable: -1 and 3. When I plugged each of those into the form y^2-2y-3=0, I got two true statements (9-9=0, and 3-3=0)

so I looked at the hints, which showed that the value -1 could not be true, because in the original equation 2y-3 = the square root of the quantity 3y^2 - 10y + 12, the result ends up being that -5 = the square root of 25. But why is this wrong? -5 * -5 does equal 25. Is there a rule by which only positive numbers can be the square root of a number, and if so, why?

Thank you for any insight anyone is able to impart.

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Drashti

2017. május 27. 7:25
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The square root of a positive number cannot be defined because we don't know if that number came by squaring -ve number or +ve number. Therefore, we write +-5 for the square root of 25.

I hope this was helpful :)
Meg

2017. május 27. 13:30
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Very helpful, thank you. Confirms that the error was indeed not mine, much to my surprise. Usually I am the one making the error, but in this case, my calculations matched that of the hints, and the only difference was that the hints said that one of the two values for the variable, y, could be ruled out due to it leading to the "false" conclusion that -5 = sq.rt 25 when in fact that is not a false statement.

Now that I know such an error can occur on Khan Academy, I will be prepared to report an error in Khan if I ever see one (after determining that the error wasn't mine, to the best of my ability).

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Aren't both 5 and -5 the square roots of 25?

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