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### Course: Get ready for Geometry > Unit 1

Lesson 7: Approximating irrational numbers- Approximating square roots
- Approximating square roots walk through
- Approximating square roots
- Comparing irrational numbers with radicals
- Comparing irrational numbers
- Approximating square roots to hundredths
- Comparing values with calculator
- Comparing irrational numbers with a calculator

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# Comparing values with calculator

Let's use the technique of squaring to compare values. We first compare 22.9% to an arbitrary value, 0.3, and then square 0.3 to compare it to the square root of 0.45. This helps us understand which value is larger without needing a calculator.

## Want to join the conversation?

- How come when he squares the square root of 0.45 it remains 0.45?(5 votes)
- 0.45 squared is 0.2025, and the square root of 0.2025 is 0.45, so basically, a square root undoes a square, and vice versa. Here's another example of this: if we find the square root of the number 9, we get 3. 3 squared is 9, so we are back to the number 9.

Hope this helps :)(30 votes)

- Why did he round up to 30%, when 22.9% is closer to 20%?(13 votes)
- In most situations, it is better to round up. Say you needed 22.9% of a gallon of concrete to finish a sidewalk. It is hard to measure 22.9% of a gallon, but if you round down to 20% of a gallon, there would not be enough concrete to finish the sidewalk, so it would be better to round to 30% of a gallon so you would have enough concrete with some left over.(8 votes)

- how is 22.9 less then 0.3? when you line up the decimals , wouldn't 0.3 be less then 22.9?(7 votes)
- It is 22.9%, so when you move the decimal two places, you get the equivalent of 0.229 which is less than 0.3.(10 votes)

- Cant you just make .45 into a percentage which would be 45% and you automatically know that its greater than 22.9%?(11 votes)
- How did he get 0.3?(10 votes)
- I'm using the on-screen calculator for first time, when I put in 8 then square root sign then = I get a pink bar across my answer window instead of an answer. What does this mean? How can I find the square root of 8 on this style of calculator?(3 votes)
- Hi! I know I'm super late, but maybe this will help someone else. Let's say you wanted to get the square root of 4. Here are the steps:

1. Click the square root symbol button

2. Click the button for number 4

3. Click the close parentheses button i.e. )

And whatever different number you have just follow these steps and replace the 4 with your different number.(12 votes)

- since when did we put a percentage into a decimal(5 votes)
- right now lol(3 votes)

- How do you find square roots without a calculator?(3 votes)
- i just randomly multiply two numbers that seem about right until i get the answer.(5 votes)

- how can you compare a percent to a square root(4 votes)
- You can convert the percent to a decimal and then square the decimal and the square root and compare....Or you don’t and quite to code on Scratch(2 votes)

- Obviously not the square root of 0.45, it's 22.5%(3 votes)

## Video transcript

- [Voiceover] 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 can think about
this without a calculator. And then use a calculator
to see which one is larger. 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 gonna pick 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 can 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 'cause it's less than 0.3. So why don't I change the problem to that? Let's compare 0.3-- 0.3 to square root-- to the square root of-- let me do that thing pink color-- to the square root of 0.45. And now I can 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, three times three is nine. 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 .09. 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 .09 is clearly less than 0.45. Or, 0.3 squared is clearly
less than square root of-- 0.3 squared is less than the
square root of 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 that 22.9%, if it's less than this,
and this is less than this, well 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 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 are two ways we can do it. We could do it 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." 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 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, would you rather have a 22.9% off the price of something?" Or, maybe some type of
new store could say, "Hey, sales! Square root
of 0.45 off of all goods." I don't know.
(chuckles) That can be an interesting thing. Could be very confusing for customers. But, anyway. Hopefully this was helpful.