Approximating square roots to hundredths | Pre-Algebra | Khan Academy

Learn how to approximate the decimal value of √45 without using a calculator.

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[jryer]

simplified version ... sqrt(x) = s + (x-r)/(y-r)
sqrt(45) = 6 + (45-36)/(49-36) = 6 + 9/13 = 6.692
x = 45, r = 36, y = 49, s = 6
x = radicand ... r = nearest perfect sq < x ... y = nearest perfect sq > x ... s = square root of r

[bysirens]

Because 45 is 9 away from 36.

He was trying to see how many numbers there were between 36 and 49.

45 was 9 away from 36, and 45 is 4 away from 49. He was just seeing how far apart they were. Hope I helped. :)

[hanashanmei]

When I learn this in my book, I'm clueless. He makes it so much easier and more comprehendible (:

[altmrrelaxed]

I was looking for the square root method with long division. I had to re-invent it to understand it. Started witn N = ( X + R )^2, expanded to ( X )^2 + ( 2( X ) + R )( R ) where X is the current approximation and R is the current next digit of the truncated value X.

[kyletezanos]

Can you please do a Newton's Method video.

[jumpydaman]

Thank you I changes schools in the middle of a lesson and I was lost.
You really help. Thx

[Besmaht]

You made my lifelong problems solved in about 10 min.

[jaisgirlfriend]

There are 13 numbers between 36 and 49. 45 is the ninth of those 13 numbers, so it is "9 of the way through" the distance, or 9/13 . (:

[NevaehBeatez]

I developed a new algorithm for solving square roots rapidly but I've never heard of this one. I like it

[test-jtel]

THANK YIOU SO MUCH MY TEACHER TAUGHT ME THIS AND I TOTALLY FORGOT THIS METHOD UR LIKE TEH ONLY PERSON ON YOUTUBE WHO USES THE SAME METHOD

[CRISNCHIPS]

@LSDjTutorials I mean, you could use Euler's Method for Linear Approximation for these problems.

[krishnac]

There is a simple solution to this problem. √45 = √5*9 = √5*3*3 = 3√5 = 6.708

[robinlavalle]

you teach me this way better than my teacher

[Ben.e]

I'm in 8th and my math teacher told us to watch this as HW.

[JonZVDK]

There has got to be an easier way to this, is there one at all?

[michaelbartonmdb]

how about using calculus to get an exact number...

[ogorangeduck]

Don't use a calculator-use a slide rule instead! It isn't considered a calculator in the modeen day.

[nickydrewplayz]

although he only helped a little a little can still shift a kid just enough to understand, im not saying everybody had trouble maybe some people have a different mind set and they did understand it but this video didn't really help me i did have to find another video to help

[NoahSkeene]

Great video, you really helped me alot!

[Kyler-]

This was a qr code on my math sheet lol but thank you