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Question Video: Finding the 𝑛th Root of a Number Mathematics

True or false: √−100 = −10.

01:24

Video Transcript

True or false: the square root of negative 100 is equal to negative 10.

One way to approach this question is to think that if we’re finding the square root of negative 100, we’re really asking, what number squared gives negative 100? Let’s consider the possibilities. We could have 10 multiplied by 10, but, in this case, 10 multiplied by 10 gives 100 and not negative 100. So let’s try negative 10 times negative 10. Well, this doesn’t equal negative 100. It equals positive 100. That’s because when we multiply two negatives together, we get a positive answer.

There are ways in which we could get negative 100. For example, we could do negative 10 times 10 or 10 times negative 10. However, we need to have the same number multiplied by itself, so neither of these would work. In fact, in general, we can’t take the square root of a negative number and get a real answer. If we look at the question, if we had the square root of 100 equals negative 10, that could be true, since we could consider the negative value of the square root. However, the answer to this question is that this statement is false.

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