prove that value of sqrt 100 - sqrt 99 lies vetween 1/18 and 1/20

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prove that value of sqrt 100 - sqrt 99 lies vetween 1/18 and 1/20

Mathematics
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we can say that sqrt99=3sqrt11=3*3.316=9.948 sqrt100=10 so 10-9.948=0.052 nw 1/18=0.55555... 1/20=0.5 so 0.052 lies between 0.55555... and 0.5 Thus,Proved!!!!!!
10 - sqrt(100-1) => 10 - 10(1 - 1/100)^1/2 now let's expand (1 - 1/100)^1/2 using binomial theorem
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@experimentX u can use binomial theorem but then hw do we know if coolbird143 knows this or not?
(1-1/100)^1/2 = 1 -1/100x1/2-(1/100)^2x1/2 - ...
well the best way is to use calculator ... :D
or use ure brains...using calculator is bad....
10 - 10(1 - 1/100)^1/2 = 10 - 10 + 1/2*10/100 + 1/2*1/2*1/2*10/10000 + 1/2*1/2*3/2*1/6*10/1000000 => 1/2*10/100 + 1/2*1/2*1/2*10/10000 + 1/2*1/2*3/2*1/6*10/1000000 ... which is a converging series that lie between 1/18 and 1/20

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