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Question
Answer the following:
Using binomial theorem, find the value of `root(3)(995)` upto four places of decimals
Solution
`root(3)(995) = (995)^(1/3)`
= `(1000 - 5)^(1/3)`
= `[1000 (1 - 5/1000)]^(1/3)`
= `10(1 - 5/1000)^(1/3)`
= `10[1 - 1/3(5/1000) + (1/3(1/3 - 1))/(2!) (5/1000)^2 - ...]`
= `10[1 - 1/600 + 1/3((-2)/3)(1/2)(1/200)^2 - ...]`
= 10[1 – 0.00167 + ...]
= 10(0.99833)
= 9.9833
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