# What is the square root of #100000#? I got as far as #100sqrt(10)#, but what is the final answer?

##### 2 Answers

#### Explanation:

So the "final answer" may be simply

If you use a calculator, it will give you an approximation like:

#sqrt(10) ~~ 3.16227766#

Hence

Note that *continued fraction* expansion:

#sqrt(10) = [3;bar(6)] = 3+1/(6+1/(6+1/(6+1/(6+1/(6+...)))))#

We can get rational *approximations* to

For example:

#sqrt(10) ~~ [3;6] = 3+1/6 = 19/6 = 3.1bar(6)#

#sqrt(10) ~~ [3;6,6] = 3+1/(6+1/6) = 3+6/37 = 117/37 = 3.bar(162)#

See explanation

#### Explanation:

Use binomial expansion

The sum to four terms is

The magnitudes of the ratio of consecutive terms is more than 10.

So, easily the sum here might be correct to 5-sd, rounded. And So #

5-sd