Puzzle of the Day [modified .2 ]
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Can You Find ROOT of a number on a standard calculator WITHOUT touching the root sign or power sign a power sign also acts like a root sign and believe me you can Easy huh! try it ? tell me the EXACT steps * Easy looking problems are sometimes the most challenging ones Rule # 17: Omit Needless Words - Strunk, William, Jr. ------------------------------------------------------------- Universal DBA | Ajax Rating -- modified at 19:15 Friday 23rd June, 2006
Easy. Defining x = ea => a = ln(x) sqrt(x) = exp(a / 2) sqrt(x) = exp(ln(x) / 2) Similarly, you can go for other roots (n) by: nth_root(x) = exp(ln(x) / n)
Ryan
"Punctuality is only a virtue for those who aren't smart enough to think of good excuses for being late" John Nichol "Point Of Impact"
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Can You Find ROOT of a number on a standard calculator WITHOUT touching the root sign or power sign a power sign also acts like a root sign and believe me you can Easy huh! try it ? tell me the EXACT steps * Easy looking problems are sometimes the most challenging ones Rule # 17: Omit Needless Words - Strunk, William, Jr. ------------------------------------------------------------- Universal DBA | Ajax Rating -- modified at 19:15 Friday 23rd June, 2006
Use of Bakhshali Formula here[^] ofcourse as suggested by ed.poore and a few others we have to do a guess work , and yes this bakshali formula is actually a version of newtons method and as you will see its uses two iterations in a single step q = A ^ 2 + b = A * A + b example 41 = 6 ^ 2 + 5 = 6 * 6 + 5 Bakhshali Formula says sqrt(q) = sqrt(A^2 + b) = A + b/(2A) - (b/(2A))^2/[2(A + b/(2A))] which comes down to Sqrt(q) = sqrt(A^2 + b) = A + b/(2A) - (b/(2*A))*(b/(2*A)) / (2*(A + b/(2*A))) sqrt(41)[^] = 6 + 5/(2*6) - ((5/(2*6))*(5/(2*6)))/(2*(6 + 5/(2*6)))[^] Mathematical operations used = /, * , + , - have a nice weekend Rule # 17: Omit Needless Words - Strunk, William, Jr. ------------------------------------------------------------- Universal DBA | Ajax Rating
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Easy. Defining x = ea => a = ln(x) sqrt(x) = exp(a / 2) sqrt(x) = exp(ln(x) / 2) Similarly, you can go for other roots (n) by: nth_root(x) = exp(ln(x) / n)
Ryan
"Punctuality is only a virtue for those who aren't smart enough to think of good excuses for being late" John Nichol "Point Of Impact"
Hey ryan Thats a great solution exp is actually the power button, i added later that without using the root ket or power key i have added a solution here[^] have a good weekend raj Rule # 17: Omit Needless Words - Strunk, William, Jr. ------------------------------------------------------------- Universal DBA | Ajax Rating
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Quartz... wrote:
but it won't give a result instantly in a calculator
Neither does the ^ or sqrt button, it performs the ln comparison to solve roots. It just happens much more quickly. Basically it all depends on how accurate you want to be.
The Welsh will always support two teams: The Welsh, and anyone playing England :)
i have added the solution its quite similar to yours here[^] have a good weekend Rule # 17: Omit Needless Words - Strunk, William, Jr. ------------------------------------------------------------- Universal DBA | Ajax Rating
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Can You Find ROOT of a number on a standard calculator WITHOUT touching the root sign or power sign a power sign also acts like a root sign and believe me you can Easy huh! try it ? tell me the EXACT steps * Easy looking problems are sometimes the most challenging ones Rule # 17: Omit Needless Words - Strunk, William, Jr. ------------------------------------------------------------- Universal DBA | Ajax Rating -- modified at 19:15 Friday 23rd June, 2006
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Use of Bakhshali Formula here[^] ofcourse as suggested by ed.poore and a few others we have to do a guess work , and yes this bakshali formula is actually a version of newtons method and as you will see its uses two iterations in a single step q = A ^ 2 + b = A * A + b example 41 = 6 ^ 2 + 5 = 6 * 6 + 5 Bakhshali Formula says sqrt(q) = sqrt(A^2 + b) = A + b/(2A) - (b/(2A))^2/[2(A + b/(2A))] which comes down to Sqrt(q) = sqrt(A^2 + b) = A + b/(2A) - (b/(2*A))*(b/(2*A)) / (2*(A + b/(2*A))) sqrt(41)[^] = 6 + 5/(2*6) - ((5/(2*6))*(5/(2*6)))/(2*(6 + 5/(2*6)))[^] Mathematical operations used = /, * , + , - have a nice weekend Rule # 17: Omit Needless Words - Strunk, William, Jr. ------------------------------------------------------------- Universal DBA | Ajax Rating
sqrt x = log x/log 2 This I will do if only the sqrt key was not working. If the log key wasn't working either, I would have flunked! Abhishek
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sqrt x = log x/log 2 This I will do if only the sqrt key was not working. If the log key wasn't working either, I would have flunked! Abhishek
AbhishekBK wrote:
sqrt x = log x/log 2
Errr... no it's not. sqrt(9) = 3 log(9) / log(2) = 3.1699250014423123629074778878956
Ryan
"Punctuality is only a virtue for those who aren't smart enough to think of good excuses for being late" John Nichol "Point Of Impact"
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AbhishekBK wrote:
sqrt x = log x/log 2
Errr... no it's not. sqrt(9) = 3 log(9) / log(2) = 3.1699250014423123629074778878956
Ryan
"Punctuality is only a virtue for those who aren't smart enough to think of good excuses for being late" John Nichol "Point Of Impact"
er........... looks like I would have flunked anyway! :laugh: Abhishek
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er........... looks like I would have flunked anyway! :laugh: Abhishek
AbhishekBK wrote:
looks like I would have flunked anyway!
Hehe :)
Ryan
"Punctuality is only a virtue for those who aren't smart enough to think of good excuses for being late" John Nichol "Point Of Impact"
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Quartz... wrote:
ROOT of a number on a standard calculator WITHOUT touching the root sign or power sign a power sign also acts like a root sign
4/2 (4 divided by 2) 2 squared is 4 the square root of 4 is 2. what did i win? :laugh: ...yeah, i heard you.
david s_ wrote:
what did i win?
Square root of -2 Rule # 17: Omit Needless Words - Strunk, William, Jr. ------------------------------------------------------------- Universal DBA | Ajax Rating