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.