Question 344619: please help me solve 9^1/4 longhand without calculator
Answer by Jk22(389)   (Show Source):
You can put this solution on YOUR website! 9^1/4=9/4 if operator priorities works,
if we want 9^(1/4)=+/-Sqrt(3) :
hand extraction algorithm :
a) like division layout, though divisor place is root place
b) the smallest square to fit in 3 is 1, 1x1=1<3, 2x2=4>3, hence root place 1.
c) 3-1=2(*)
d) descend 2 digits: .00, place after 2(*), 2.00
e) descend root on the right, times 2
f) find the biggest n such that 2nxn<=2.00, 21x1=21, 22x2=44, 23x3=46,..
find 27x7=189, 28x8=224>200
repeat from (c) : looks like :
3.00__ | 1.7320
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1.00__ |
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2.00(*)| 27x7=140+49=189, 28x8=160+64>200, hence digit 7
1.89__ |
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110.0_| 2x17=34, 343x3=900+120+9=1029<1100, 344x4=1200+..>1120, hence digit 3
102.9_|
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710.0_| 2x173=346, 3462x2=6924<7100, 3463x3>7100, hence digit 2
692.4_|
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1760.0| 2x1732=3464, 34641>17600, hence digit 0
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