Answer:
1.732, 2.646, 3.317, 5.099, etc.
Then you just have to plot them on a number line.
Explanation:
I'll assume you know how to use a number line, and how to represent numbers on it, even decimal numbers. Because I can't really show you how to do that here.
And I'll assume you know what "square root" means, but I'll just go ahead and say that it means, "What number, multiplied by itself, gives me this number?"
So when they ask, "First, tell which two whole numbers the square root is between," that should be easy: do the square root on your calculator and then pick the integer that's lower than that result, and the one that's higher.
So for example the square root of 3 is 1.732 (rounded to 3 decimal places like the question specifies). What "whole numbers" is that between? 1 and 2, of course. Good on that?
But you don't even need a calculator for that part. Let's work on the square root of 7:
- Is it going to be bigger than 2? Yes, because 2 times 2 is 4, and that's less than 7.
- Is it going to be bigger than 3? No, because 3 x 3 = 9, which is more than 7.
- So
is bounded by 2 & 3.
You could pretty quickly do all of them like that and then put a little dot on a number line between those integers. But it wants precision to 3 places, so you might as well just do it on the calculator and then say what two digits it's between.
So here are the first few square roots, to 3 digits:
1.732
2.646 <--this one rounded UP
3.317 <-- and this one
5.099
5.831
etc.
Are you struggling with how to plot those? If so, it's easy. Let's take 1.732:
- It's between 1 and 2, of course.
- And it's 7-tenths of the way between them. That's what the 0.7 means.
- That may get you close enough, but if you need more precision, use the 0.03 piece to say that it's 3-tenths of the way between 0.7 and 0.8.
- You could use the 0.002 bit to say that it's 2-tenths of the way between 0.73 and 0.74, but you likely can't even see that on your number line.