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CCSS.Math:

let's see if we can solve the equation P squared is equal to zero point eight one so how could we think about this well one thing we could do is we can say look if P squared is equal to zero point eight one 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 zero point eight want 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 the P is equal to the plus or minus square root of zero point eight one which kind of helps us that's another way of expressing the same the same equation but still what could P be and your brain you might immediately say well okay you know if if this was P squared is equal to 81 I kind of 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 the 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 going to 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 a zero point nine squared let me try that out zero I'm using a different color so let's say I took a zero point nine squared zero point nine squared well that's going to be zero point nine times 0.9 which is going to be equal to well 9 times 9 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 zero point eighty one in fact we could write zero point eighty one is zero point nine 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 zero point eight one I can write that is 0.9 squared in fact I could also write that as negative 0.9 squared because if you put a negative here and a negative here it's still not going to change the value negative times a negative is going to be a positive I could actually I want to 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're taking the positive and negative square root so this is going to be P 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 0.8 1