The value of (994)1/3 according to binomial theorem is
Answers 2
Answer:
[tex](994)^{ \frac{1}{3} } \\ \\ (1000 - 6)^{ \frac{1}{3} } \\ \\ \bigg \{1000 \bigg( 1 - \frac{6}{1000} \bigg ) \bigg \}^{ \frac{1}{3} } \\ \\ \bigg \{10 ( 1 - 0.006 ) \bigg \}^{ \frac{1}{3} } \\ \\10 \bigg ( 1 - \frac{1}{3} \times 0.006 \bigg) \\ \\ 10(1 - 0.002) \\ \\ 10(0.998) \\ \\ \bf 9.98[/tex]
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Author:
cirortxb
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Given:
(994)^1/3
To Find:
Find the value using the binomial theorem
Solution:
When the power of the algebraic expression increases it becomes lengthy to find the value like (x+3)^66 is very hard to calculate that why we use binomial theorem for the expansion of term with greater powers or fractions, a binomial expansion should only contain two not similar terms if the power of the expansion is n then the total number of terms in the expansion will be (n+1).
The formula for expansion if the power is in the fraction is,
If n is negative or fraction also |x|<1, then the expansion will be,
[tex](1+x)^n=1+nx+\frac{n(n-1)}{2!}x^2 +\frac{n(n-1)(n-2)}{3!}x^3 +...[/tex]
Now to find the value of (994)^1/3, we will go as
[tex]=(994)^{1/3}\\=(993+1)^{1/3}\\=1+\frac{993}{3}+\frac{\frac{1}{3} *\frac{-2}{3} }{2!}*993*993+\frac{\frac{1}{3}*\frac{-2}{3} *\frac{-5}{3} }{3!}*993*993*993+...\\=1+331-54780.5+60441151.67-...\\=9.97[/tex]
Hence, the value of (994)^1/3 is 9.97.
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Author:
cobwebrchv
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