It is ##pm9##.
##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.
Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Ask A Question and we will direct you to our Order Page at WriteDemy. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Fill in all the assignment paper details that are required in the order form with the standard information being the page count, deadline, academic level and type of paper. It is advisable to have this information at hand so that you can quickly fill in the necessary information needed in the form for the essay writer to be immediately assigned to your writing project. Make payment for the custom essay order to enable us to assign a suitable writer to your order. Payments are made through Paypal on a secured billing page. Finally, sit back and relax.
About Writedemy
We are a professional paper writing website. If you have searched a question and bumped into our website just know you are in the right place to get help in your coursework. We offer HIGH QUALITY & PLAGIARISM FREE Papers.
How It Works
To make an Order you only need to click on “Place Order” and we will direct you to our Order Page. Fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Are there Discounts?
All new clients are eligible for 20% off in their first Order. Our payment method is safe and secure.