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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..
 one year ago
 one year 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..
 one year ago
 one year ago

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asnaseerBest ResponseYou've already chosen the best response.2
since 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.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
another 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:\[(9+b)^2=82\]
 one year ago

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

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

asnaseerBest ResponseYou've already chosen the best response.2
yes, 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.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
have you heard of the NewtonRaphson method?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
if you have, then that will converge to the answer faster.
 one year ago

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

aroubBest ResponseYou've already chosen the best response.0
Okay, 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
 one year ago

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

aroubBest ResponseYou've already chosen the best response.0
Yeah and I think you have to round it at the end right?
 one year ago

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

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

asnaseerBest ResponseYou've already chosen the best response.2
so 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.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
does that make sense?
 one year ago

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

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

asnaseerBest ResponseYou've already chosen the best response.2
remember 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'
 one year ago

aroubBest ResponseYou've already chosen the best response.0
This is even more complicated lol but yeah i understood how =) Thank youu!!
 one year ago
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