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### Course: Grade 8 math (FL B.E.S.T.)>Unit 2

Lesson 4: Approximating irrational numbers

# Approximating square roots

Learn how to find the approximate values of square roots. The examples used in this video are √32, √55, and √123. The technique used is to compare the squares of whole numbers to the number we're taking the square root of.

## Want to join the conversation?

• what to do to get an exact answer for square root of 55
• The thing is, you can't, since it's irrational. What you can do is simplify the square root, say the √55 is the answer, or just enter it in a scientific calculator for the most precise approximate.
• Is there an advanced way to do it when you get older since the approximation is really just an irrational number that goes on, or do we stick with approximating like this throughout our entire lives?
• I'm not sure that there's a more advanced way, but it's definitely good to know how to approximate like he describes in the video - while it's convenient to use a calculator, it's even better to know that the value the calculator gives you is close to what you have already approximated.

If you go on to upper level math, physics, engineering, etc., it is so helpful if you already have strong skills in estimating / approximating. Alot of people will be able to roughly estimate the answer in their heads - even for complicated problems - before they sit down to work it out on paper. It's really amazing.

As far as square roots are concerned, you can definitely memorize a few (or a lot), but you won't be able to memorize them all. So the ability to approximate the value of a square root - to be able to look at it, and have a rough idea of the value - is really handy.
• How do you know what 32 is between?
• The closest bigger number that has a perfect square, and the closest smaller number that has a perfect square.
• Wait! It could be between a decimal right, because I got a answer that is between a decimal in Khan Academy's Approximating square roots practice.
• uhm can someone tell me how to find the square root of an imperfect square..cos I have this thing for homework and idk what's the square root of 1825..like is there a formula for finding the square root?
• unless you want to approximate, just leave it with the imperfect part inside the root, like such

root(1825) is root(5*5*73) so it simplifies to 5 √(73), or five times the square root of 73. just leave the 73 inside the root sign, and leave the five outside.
• What's the approximate square root of pi?
• The square root of pi, to two decimal places, is approximately 1.77.

Have a blessed, wonderful day!
• I've been able to answer a few questions here but I also have a question :P This lesson is for finding approximate, and with smaller numbers. With my book it asks for something as big as the square root of 67392.

I've done some googling, but I struggle to understand the steps to doing the long division by seperating the number into pairs of two, then finding the biggest square that can fit, then subtracting that for it etc.

Is there a better way, or could someone please explain so that it can make sense? Thanks y'all :)

- Apex
• So for your example of 67392, find the prime factorization then take the square root. It would be sqrt(2^6 * 3^4 * 13) which can be simplified to 2^3 * 3^2 * sqrt(13) = 72sqrt(13). Then approximate sqrt(13) and multiply. Hope this makes sense!
• I Don't Get This. Is 32 Square Rooted 5 or 6? Is It Neither or Both? I'm Really Confused Right Now, I Know Sal's A Great Teacher, Makes It Easier And Everything, But This Video Was Hard To Understand. Is It Just Me? Please HELP!!
• The square root of 32 is neither 5 nor 6. It is greater than 5 but less than 6.

Have a blessed, wonderful day!
• At he says 123 is 123 when you square it, what does he mean?
• What Sal did there is he squared a square root/that √ symbol you saw.

A square root is essentially trying to figure out what number multiplies/squares in order to get the number we're square rooting. If that's true, then by the same logic if we were to square a square root we would just end up with the number underneath that symbol.

(If this is confusing, think of the entire square root as like a variable of sorts representing its answer (like √25=5) and then imagine what would happen if we were to square that answer (which is already the square root), ending up whith whatever is under the radical (√25=5, 5^2=25). In other words, the symbol represents that we're trying to find what times itself = that number, but by squaring the whole thing we're just undoing whatever we decided to do.)