:) HI!!!!!! PLZ HELP WITH SQUARE ROOTS!!! (ps yes im lillybeth)

[lillybeth123]

Hey guys, I need help figuring out a square root problem:


So I already know how to figure out square roots and the hypotenuse and stuff, but only with a calculator.

So lets say that this is the problem:

10, 10, - Find the hypotenuse.
So I already know that A2 + B2 = C2.

Which means that 10(2) + 10(2)=
100 + 100= 200

So to find the answer, you find the square root of 200 (I think), and I know how to do that on a calculator, but how do you do it without one? Is there a faster way than just multiplying random numbers?? Thanks!

 

[Bob Brown MSEE]

To get Square Root of N...

1) Choose a guess, we'll call it G
2) Get a better guess from the following formula.

Better guess = (G²+N)/(2G)

 

[HallsofIvy]

Hey guys, I need help figuring out a square root problem:So I already know how to figure out square roots and the hypotenuse and stuff, but only with a calculator.So lets say that this is the problem: 10, 10, - Find the hypotenuse.So I already know that A2 + B2 = C2.Which means that 10(2) + 10(2)= 100 + 100= 200So to find the answer, you find the square root of 200 (I think), and I know how to do that on a calculator, but how do you do it without one? Is there a faster way than just multiplying random numbers?? Thanks!

How, exactly are you required to give the answer? You can simplify \(\displaystyle \sqrt{200}\) by writing it as \(\displaystyle \sqrt{2(100)}= 10\sqrt{2}\). Any more than that, for example, remembering that \(\displaystyle \sqrt{2}\) is about 1.414 will let you say that \(\displaystyle \sqrt{200}\) is about 14.14. But any numerical value will be only approximate while \(\displaystyle \sqrt{200}\) or \(\displaystyle 10\sqrt{2}\) are exact.


If you really need a reasonably quick way to find the square root of 200, try this: you should know that \(\displaystyle 14^2= 196\) and \(\displaystyle 15^2= 225\) so that the square root of 200 is between 14 and 15. So try 14.5, half way between. \(\displaystyle 14.5^2= 210.25\) so the square root is between 14 and 14.5. Again, try half way between, 14.25. \(\displaystyle 14.25^2= 203.0625\) so the square root of 200 is betwee 14 and 14.25. Try half way between, 14.125. \(\displaystyle 14.125^2= 199.515625\). That is slightly less than 200 so the square root of 200 is between 14.125 and 14.25. Continue determining two numbers whose squares are on either side of 200 and try half way between them for the next approximation until you are getting an accurate enough result.