Question

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

Answer 1

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!!!!!!

Answer 2

10 - sqrt(100-1)
=> 10 - 10(1 - 1/100)^1/2
now let's expand (1 - 1/100)^1/2 using binomial theorem

Answer 3

Hello guest please sign in or sign up...Thnk u!!:D

Answer 4

@experimentX u can use binomial theorem but then hw do we know if coolbird143 knows this or not?

Answer 5

(1-1/100)^1/2 = 1 -1/100x1/2-(1/100)^2x1/2 - ...

Answer 6

well the best way is to use calculator ... :D

Answer 7

or use ure brains...using calculator is bad....

Answer 8

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