How to determine the value? Show me the workings?
Don't ask me to use a calculator..This question came out in paper 1 where calculator is not allowed.
2007-10-27 14:58:45 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
(1) First note following facts:
sqr(144) = 12; so sqr(1.44) = 1.2
sqr(121) = 11; so sqr(1.21) = 1.1
(2) Second note these approximations (these are well-known or obvious):
sqr(2) ~ 1.414
pi ~ 22/7
2^(1/7) ~ 2^(1/8)
(3) Now from (1) and (2) we make the following approximation:
2^(1/8)
= sqr (sqr (sqr (2))
~ sqr ( sqr (1.414))
~ sqr (sqr (1.44))
~ sqr (1.2) ~ sqr (1.21)
~ 1.1
(4) Now...we are ready to calculate a good approximation for 2^pi (without a calculator!).
2^pi
~ 2^(22/7)
= (2^3)(2^(1/7))
= 8*(2^1/7)
~ 8 (2^(1/8))
~ 8 (1.1)
~ 8.8
So 2^pi is approx. 8.8. I think this is a real good estimate.
2007-10-27 17:05:26 · answer #1 · answered by Chang Y 3 · 0⤊ 0⤋
Well you'd have to multiply 2 by itself 3.14 times.
So without doing any math, really, you know it will be slightly bigger than 8.
2007-10-27 22:09:12 · answer #2 · answered by Lady Geologist 7 · 0⤊ 0⤋
(pi)=3.1416
2(pi)=3.1416 X 2, =6.2832
2007-10-27 22:23:49 · answer #3 · answered by Grampedo 7 · 0⤊ 2⤋