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CCSS.Math:

my question to you is which of these two values is greater 22.9% or the square root of 0.45 and I encourage you to first try to see if you could think about this without a calculator and then use a calculator to see what what which one is larger so let's first try to do it without a calculator so one thing that you could try to say is well look you could say that 22.9% that's going to be less than I'm just going to pick an arbitrary an arbitrary number here let's say that's less than 30% so that's going to be less than and I picked 30% because it's easy to calculate 30% or the square of 30% so that's less than 30% or it's another way of saying that's less than 0.3 0.3 and then we could try to compare 0.3 to this thing here and if 0.3 is less than this well then 22.9% is going to be less than this because it's less than 0.3 so why don't I why don't I change the problem to that let's compare 0.3 0.3 to square root 2 the square root of let me do that same pink color to the square root of 0.45 and now I could use the squaring technique what happens if I square each of these quantities if I Square this 0.3 times 0.3 let's see 3 times 3 is 9 but you're multiplying two things that each have one digit to the right so you're gonna have two digits to the right so it's going to be 0.9 and if you were to square this over here I'll just keep using the white if you were to square this right over here what's that going to be well that's just going to be 0.45 so 0.9 is clearly less than 0.45 or 0.3 squared is clearly less than square root of 0.5 0.3 squared is less than the square root of 0.5 0.45 squared and so we know that 0.3 is going to be less than is going to be less than the square root of 0.45 and so now we can say the 22.9% if it's less than this and this is less than this well then 22.9% must be less than that now another way you can do it you could take out a calculator you could take out a calculator I'll do that just just for kicks so let me get the calculator out so 22.9% that's the same thing as that's the same thing as 0.229 so we really just want to compare this quantity to the square root of 0.45 and there's two ways we could do it we could do the way I started you could square this and see if it's greater than 0.45 so let's do that you could just square it and you see no it's zero this is zero point this is 0.05 which is clearly less than 0.45 and so that would validate this or you could do it the other way around you could just use your calculator to calculate the square root of this so you could say 0.45 and then take the square root the square root of this value right over here is approximately is approximately 0.67 so this is this thing right over here is approximately 0.67 which is approximately 67% which is clearly greater than 22.9% so a bunch of ways that you could approach it it is nice to be able to estimate things think in your head so that if you didn't have access to a calculator you could get a general sense of hey you know would you rather have a twenty two point nine percent off the price of something or maybe maybe some type of new store could say hey sale square root of 0.45 off of all goods I don't know that could be an interesting thing could be very confusing for for customers but anyway hopefully this was helpful