# How do you find the square root of 81?

It is ##pm9##.

Don't use plagiarized sources. Get Your Custom Essay on
How do you find the square root of 81?
Just from \$13/Page

##81=9*9## then the square root of ##sqrt(81)=9##.
Because the double multiplication for the same sign is always positive, the square root is also valid with the other sign ##81=(-9)*(-9)## then ##sqrt(81)=-9## and we can say that ##sqrt(81)=pm9##.

What if we do not know the value? There is an algorithm to calculate the square root quite simple (the Babylonian algorithm).

We want to calculate the square root of ##81##, we first guess a possible value. For example we know that ##10*10=100## and ##7*7=49##, then we can imagine that the square root of ##81## is between ##7## and ##10##, we can imagine for example ##8.3##.

Then the algorithm tell us that the next step of approximation is given by

##x_(n+1)=1/2(x_n+alpha/x_n)## where alpha is the number that we are searching the square root (for us ##alpha=81##) and ##x_n## is our guess. Our first guess is ##x_1=8.3##, then the next step of approximation is

##x_2=1/2(8.3+81/8.3)=9.029518##.

I continue with the next approximation

##x_3=1/2(9.029518+81/9.029518)=9.0000482##

##x_4=1/2(9.0000482+81/9.0000482)=9.00000000013##

##x_5=1/2(9.00000000013+81/9.00000000013)=9## (my computer does not approximate more).

As you can see in few steps the algorithm converges to the square root. Of course, because the previous discussion about the positive and negative sign, also the same result with the minus sign is a solution of the square root.

For me it is very fascinating the fact that I can write on Socratic.org, on Internet, an answer to someone that I do not know and that probably lives in a place that I will never see in my life, an algorithm to calculate the square root of a number invented 4000 years ago by some very clever Babylonian. Mathematics is the most universal language, trough space and time.

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

### Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Order your essay today and save 15% with the discount code BANANA