Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. 1.a.)use the assumed babylonian square root algori

1.a.)Use the assumed Babylonian square root algorithm (also known as Archimedes’ method) √ a 2 ±...

50.1K

Verified Solution

Question

Advance Math

1.a.)Use the assumed Babylonian square root algorithm (alsoknown as Archimedes’ method) √ a 2 ± b ≈ a ± b/2ato show that √ 3 ≈ 1; 45 by beginning with thevalue a = 2. Find a three-sexagesimal-place approximation to thereciprocal of 1; 45 and use it to calculate athree-sexagesimal-place approximation to √ 3.

1.b)An iterative procedure for closer approximations to thesquare root of a number that is not a square was obtained by Heronof Alexandria (ca. 75 CE). In his work Metrica he merely states arule that amounts to the following in modern notation: If A is anon square number, and a^2 is the nearest perfect square to it, sothat A = a^2 ± b, then approximations to √ A can be obtained usingthe recursive formula:

x0 = a

xn = 1/2 ( Xn−1 + A/( Xn−1)), n ≥ 1

(i) Use Heron’s method to find approximations through n = 3 to √720 and √ 63.

(ii) Show that Heron’s approximation x1 is equivalent to theBabylonian’s square root algorithm.

Answer & Explanation Solved by verified expert
3.6 Ratings (504 Votes)
SOLUTIONGiven That data Use the assumed Babylonian square    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Chemistry
1.2K views

i have data, Acid is HCl and base is NaOH â–³H=mCh2o(Ti-Tf) i am looking for the mass(m)...

Accounting
1.2K views

Below are several transactions for Meyers Corporation for 2021. Issue common stock for cash, $49,000. Purchase building and...

Chemistry
1.2K views

The following is a list of drugs. For this assignment, use any resources available to you...

Advance Math
1.2K views

Consider the relation T on the set of all undergraduate TAs (UTA) for the CSE department...

General Management
1.2K views

You should analyze the managerial activities and issues in the real business environment on PepsiCo. Give...

Physics
1.2K views

A cyclist is riding at speed of 10 m s takes a turn on a...

Accounting
1.2K views

Please provide the answer in your own wording in 500 words! Thank you so much...

Accounting
1.2K views

Holiday, Inc.s inventory of $887,000 at December 31, 2017, was based on a physical count...

Accounting
1.2K views

Actividad 2: Job Costing ROBLES and Associates, a C.P.A. firm, uses job order costing to...

Accounting
1.2K views

How the banana industry control its supply chain from riping to consumer consumption

Accounting
1.2K views

On January 1, 20X6, Mark Corporation issued $100,000 of 10% ten-year bonds. The bonds were...

Accounting
1.2K views

Jones Company reported pretax book income of $407,000. Included in the computation were favorable temporary...