Is √64\sqrt{64} considered 88? or is it 8,−88,-8?

Last year in Pre-Algebra we learned about square roots. I was taught then that
64=8 and 100=10, which I understood and accepted. I was also taught that ±64=8,8 because both of those numbers squared is 64, which I also get.
But this year, with a new school and teacher in a different state, our teacher is telling us that:
64=8,8 and ±64 also is 8,8. The way to get the positive root of something is:

And these seem to contradict each other. I was always taught that a regular square root returned a positive number and only a positive number, but now my teacher is saying a regular square root gives two numbers, and considering the square root of a number n is defined as
y2=n I see where he is coming from.

Upon researching this Wikipedia says:

For example, 4 and 4 are square roots of 16 because 42=(4)2=16

And Wolfram MathWorld says:

Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are 3 and +3

But on the other side, Wolfram Alpha, when given “The square root of 9” gives only 3.

So, which is right? Is 64 considered 8? or is it 8,8?


Your new teacher is wrong. is the principal square root operator. That means it returns only the principal root — the positive one. 64=8. It does NOT equal 8.

On the other hand, the equation 64=x2 DOES have 2 solutions: x=8 or x=8. Thus both 8 and 8 are square roots of 64.

Let’s see what happens when we take the principal square root of both sides of this equation: 64=x264=x28=|x|x=8 or x=8

Thus the fact that the principal square root operation throws out the negative root isn’t much of a problem as the math still works out correctly.

Source : Link , Question Author : Nico A , Answer Author : got it–thanks

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