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Evaluate (1001)^(1/3) upto six places of...

Evaluate `(1001)^(1/3)` upto six places of decimal.

Text Solution

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`(100)^(1//3) = (1000 +1)^(1//3) = [1000(1+(1)/(1000))]^(1//3) = 10 (1+001)^(1//3)`
`= 10 [ 1+(1)/(3)(0.001)+((1)/(3)((1)/(3) - 1))/(2!) (.001)^2 +….] = 10 [ 1 + 0.0003333 - (1)/(9)(0.000001)+…..`
`=10[1+ 0.00003333- 0.0000001]`
` = 10.003332`
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