Question

Describe how you would estimate the square root of a number that is not a perfect square without using a calculator. (2 points)

Answer 1

relate it to the closest perfect square root there is...for example \[\sqrt{50}\] you know the square root of 49 is 7 so you know it has to be close to 7.

Answer 2

does that make sense @ktlyn9

Answer 3

but would it be simplier if we broke that big number down? like 50 it would be like \[\sqrt{25*2}\] and then\[5\sqrt{2}\]

Answer 4

Using the Newton´s Method

Relate the square root to a function , and find the ecuation of the tangent line in a point that you supose is close to the root of that function.

For example , find the square root of 5

make F(x)= x^2-5
Of course the square root of must be close to the square root of 4, so pick 2 as you initial value, then find the tanget line there, wich has slope f´(2)= 4, at the point (2,-1),
so the ecuation os that line is y+1=4(x-2)

Then solve for y=0 and you get x=9/4

Wich is aproximadely the square root of 5.
Of course you can get most precisely aprox, repeating the process.

Answer 5

@hereweg0 Yes Thank you! Sorry I didnt reply.

Answer 6

oh ok welcome.