How to find Square Root of Number without a Calculator

[Zarunias]

I suggest everyone to look up the procedure of how to take square roots by hand. It was never teached in school to me but I was shocked when I realized that it's much easier than you would think.

[kevinsolari]

The maths behind it is worth noting and not difficult: we have 20 as a close estimate so have (20+d)²= 410
So 400 + 2×d×20 + d²= 410. But if 20 is close then d is small and d² much smaller, so can be ignored.
So d = (410-400)/(2×20)

[mdo]

You're a lifesaver. Thank you from all my heart!❤

[danstark]

This is much better. I usually estimated by doing associating squaring.

[oscarmartinpico]

even closer and closer 20 + 10/(2x20) - (10/2)^2/20^3. It is a McLaurin development or formule. The closer is the number to a root of a number known because its easy calculation, the better is the aproximation.

[Hello_all]

Thanks for this wonderful technique it's very helpful....😊

[danbentzvi]

I actually have a more precise method, but it involves additional steps. 😅 I managed to calculate the exact value up to the third decimal place.

[HarshitGoyalStudent]

This is bionomial approximation So acc. to binomial aprox.
( 1+a)^n ≈ 1+an
Smaller the value of more accurate the result is
In this question
(410)^(0.5)= (400+10)^(0.5)
Or 20(1+10/400)^(0.5) ≈
20(1+5/400) = 20.25

[MoScocious]

as someone with an auditory processing disorder, I genuinely appreciate the inclusion of captions. However, yours are sitting right over the numbers and I can't see what you're doing.

[moeberry]

It’s an overestimate because the line lies tangent above the sqrt(x) function since it’s increasing concave down.

[christianmosquera]

Excellent video wonderful 😊😊😊😊😊😊😊❤❤❤❤❤❤

[aliabdalrahman]

Ive tryed it many times its right method bro you are genius

[thebasketballchannel]

prove:
any number could be rewritten as a^2+b
thus, we could let the number be x, so we have

x=a^2+b
x-a^2=b
(sqrt(x)+a)(sqrt(x)-a)=b
sqrt(x)-a=b/(sqrt(x)+a)
sqrt(x)=a+(b/(sqrt(x)+a)))

but since sqrt(x) is a+(b/(sqrt(x)+a))), we can get an infinite series

sqrt(x)=a+(b/a+a+(b/a+a+....)
or simplified


where a is the closest perfect square and b is the distance to the perfect square

[foryoureyesonly]

Mahusay ka magturo sa Math...saludo ako!

[uamdbro]

Very nice. Would be nice to show the logic/derivation, but might be a bit too much for a short.

[mrmimi]

And there's me how calculated it mentally and somehow it was a little bit close to this methode

[eccentrico]

let f(x)=√x, a=some number, f(a)=√a, f'(x)=1/2√x, f'(a)=1/2√a

Linear approximation tells us
L(x)=f(a)+f'(a)(x-a)

And we should accept
L(x)≈f(x)

[christopherellis]

Margarine's original recipe was tallow-based. 😊

[ggxsky]

Sir please help
If F(X) = 1/√2x-1
Then
F-1(-1) is defined or undefined

[ricardofilipe]

would it fall short for sqr(2) ?
As the closest is sqrt(1) which is one so we would have 1 + (2-1)/ (2*1) which results in 1, 5 if my math hasn't failed (which might) but sqr(2) Is around 1, 41 might mislead would there be a better way for this case?