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# Square root of decimal

Video transcript

- Let's see if we can solve the equation P sqaured is equal to 0.81. So how could we think about this? Well one thing we could
do is we could say, look if P squared is equal to 0.81, another way of expressing
this is, that well, that means that P is going to be equal
to the positive or negative square root of 0.81. Remember if we just wrote
the square root symbol here, that means the principal root, or just the positive square root. But here P could be positive
or negative, because if you square it, if you square
even a negative number, you're still going to
get a positive value. So we could write that P is equal to the plus or minus square root of 0.81, which kind of helps us, it's another way of expressing the same,
the same, equation. But still, what could P be? In your brain, you might
immediately say, well okay, you know if this was P
squared is equal to 81, I kinda know what's going on. Because I know that nine
times nine is equal to 81. Or we could write that nine
squared is equal to 81, or we could write that nine is equal to the principal root of 81. These are all, I guess,
saying the same truth about the universe, but what about 0.81? Well 0.81 has two digits behind,
to the right of the decimal and so if I were to
multiply something that has one digit to the right of
the decimal times itself, I'm gonna have something with two digits to the right of the decimal. And so what happens if I
take, instead of nine squared, what happens if I take 0.9 squared? Let me try that out. Zero, I'm gonna use a different color. So let's say I took 0.9 squared. 0.9 squared, well that's going to be 0.9 times 0.9, which is going to be equal to? Well nine times nine is 81,
and I have one, two, numbers to the right of the decimal,
so I'm gonna have two numbers to the right of
the decimal in the product. So one, two. So that
indeed is equal to 0.81. In fact we could write
0.81 as 0.9 squared. So we could write this,
we could write that P is equal to the plus or
minus, the square root of, instead of writing 0.81, I could write that as 0.9 squared. In fact I could also write
that as negative 0.9 squared. Cause if you put a negative
here and a negative here, it's still not going to change the value. A negative times a negative
is going to be a positive. I could, actually I would
have put a negative there, which would have implied a negative here and a negative there. So either of those are going to be true. But it's going to work out for us because we are taking the
positive and negative square root. So this is going to be, P is going to be equal
to plus or minus 0.9. Plus or minus 0.9, or we could write it that P is equal to 0.9, or P could be equal to negative 0.9. And you can verify that, you would square either of
these things, you get 0.81.