A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
14 Find a decimal approximation to the nearest tenth:
i) √82
Is there ANY easy way other than:
Find the perfect squares that is before and after the number 82 and then add the both numbers and blah..blah..
 2 years ago
14 Find a decimal approximation to the nearest tenth: i) √82 Is there ANY easy way other than: Find the perfect squares that is before and after the number 82 and then add the both numbers and blah..blah..

This Question is Closed

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2since it is to the "nearest tenth" you won't have many numbers that you need to try. start with 9 since 9*9=81 and increase by one tenth until you get an answer that is closest to 82.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2another possible method might be to use the fact that:\[(a+b)^2=a^2+2ab+b^2\]so set a=9 and you need to find b such that:\[(9+b)^2=82\]

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2therefore:\[(9+b)^2=81+2*9*b+b^2=81+18b+b^2\]therefore:\[81+18b+b^2=82\]therefore:\[b^2+18b=1\]then try b=0.1, 0.2, ....

aroub
 2 years ago
Best ResponseYou've already chosen the best response.0Oh cool =) Can you do this method if they asked you " Find a decimal approximation to the nearest hundredth" ? @asnaseer

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2yes, then you would need to try b=0.01, 0.02, etc. However, this might take too long, so a better strategy in this case might be to use a technique where you keep halving the interval, e.g.: try b=0.50 > if this is too low, then try b=0.75 > otherwise try b=0.25 that will converge quicker.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2have you heard of the NewtonRaphson method?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2if you have, then that will converge to the answer faster.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2no worries  just use one (or more) of the techniques mentioned above to see which one you prefer.

aroub
 2 years ago
Best ResponseYou've already chosen the best response.0Okay, I got a bit stuck using your method.. My method is SOOOOO complicated. Anyway, right you said you try b=0.1,0.2.. like this: b^2+18b=1 0.1^2=18(0.1)=1 ? and if it didnt work you try 0.2 and if didnt work you try 0.3 and so on? O.o

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2you won't find an exact answer  you are supposed to find the nearest answer to one tenth

aroub
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah and I think you have to round it at the end right?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2ok, let me try and explain. we said we can rearrange the question to this form:\[b^2+18b=1\]

aroub
 2 years ago
Best ResponseYou've already chosen the best response.0but my question is you substitute b with 0.1 like that? until you find an answer to the nearest tenth?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2so what we need to do is to find what value of b will give an answer that is "closest" to 1. we can rearrange further to get:\[b^2+18b1=0\]so now we need to find a value for b that gives the closest answer to zero. so, lets try b=0.0, we get \(b^2+18b1=1\) so, lets try b=0.1, we get \(b^2+18b1=0.81\) so, lets try b=0.2, we get \(b^2+18b1=2.64\) so the "closest" answer is when b=0.1 therefore, the answer is 9.1 to nearest tenth.

aroub
 2 years ago
Best ResponseYou've already chosen the best response.0It makes sense till so the "closest" answer is when b=0.1 and then how did it become 9.1?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2because we started this from:\[(9+b)^2=82\]now we have found 'b', answer is '9+b'

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2remember we said \(9^2=81\) and we are trying to find a number that, when squared equals 82. so that number must be 9 plus a little bit. we called that "little bit" 'b'

aroub
 2 years ago
Best ResponseYou've already chosen the best response.0This is even more complicated lol but yeah i understood how =) Thank youu!!
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.