The value of ( 1003 )^1/3 according to binomial theorem is ?
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Rewrite 9993 as (103−1)3 and apply the binomial theorem to find that
9993=997002999
Explanation:
The binomial theorem states that (a+b)n=n∑k=0(nk)an−kbk
where (nk)=n!k!(n−k)!
For this problem, we will only need to calculate for n=3, and we will find that (30)=(33)=1 and (31)=(32)=3
(Try verifying this)
Noting that it is much easier to calculate powers of 10and 1 compared to 999, we can rewrite 999 as
9993=997002999
Explanation:
The binomial theorem states that (a+b)n=n∑k=0(nk)an−kbk
where (nk)=n!k!(n−k)!
For this problem, we will only need to calculate for n=3, and we will find that (30)=(33)=1 and (31)=(32)=3
(Try verifying this)
Noting that it is much easier to calculate powers of 10and 1 compared to 999, we can rewrite 999 as
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