How to find the square root of 39

Question

anonymous · Answer

you have to use a calculator. the answer would be 6.2

anonymous · Answer

I know what the answer is but i want to know how to find it?

anonymous · Answer

Please help its important

anonymous · Answer

You can use Newton's method.

amoodarya · Answer

$$\sqrt{x^{2}+a }\approx x+\frac{ a }{ 2x }\ \sqrt{39}=\sqrt{36+3}=\sqrt{6^2+3}\x=6\a=3\sqrt{6^{2}+3 }\approx 6+\frac{ 3 }{ 2(3)}$$

anonymous · Answer

I am in 9th grade

parthkohli · Answer

lol

anonymous · Answer

Okay, so first you realize: $$
36<39<49 \
6<\sqrt{39}<7
$$

anonymous · Answer

Next you can try guessing and checking: $$
6.5^2 = 42.25
$$Too high... $$
6.2^2 = 38.44
$$Too low... $$
6.25^2 = 3.90625
$$Getting closer

anonymous · Answer

I didn't get u

anonymous · Answer

that's cause no teacher would expect u to get that without a calculator...

anonymous · Answer

see as i said before i want to know the method not the answer

anonymous · Answer

those are the only ways possible.. what class is this for?

anonymous · Answer

9th

anonymous · Answer

Heron's Formula

phi · Answer

There is a method to find the square root "by hand", but I don't think it is taught nowadays.
either leave the answer written as $ \sqrt{39}$ or  use a calculator

phi · Answer

FYI, here is an example of the algorithm (notice it is a bit complicated) http://johnkerl.org/doc/square-root.html

anonymous · Answer

Long and tedious method. Anyway, here it is.|dw:1404076356935:dw|