Maharashtra State BoardHSC Science (General) 11th
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Use binomial theorem to evaluate the following upto four places of decimal 1263 - Mathematics and Statistics

Sum

Use binomial theorem to evaluate the following upto four places of decimal

`root(3)(126)`

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Solution

`root(3)(126) = (126)^(1/3)`

= `(125 + 1)^(1/3)`

= `[125(1 + 1/125)]^(1/3)`

= `(125)^(1/3) (1 + 1/125)^(1/3)`

= `5[1 + 1/3(1/125) + (1/3(1/3 - 1))/(2!) (1/125)^2 + ...]`

= `5[1 + 1/375 + 1/3(-2/3)(1/2)(1/15625) + ...]`

= 5 [1 + 0.00266 – 0.000007 + ... ]

= 5 (1.00266) = 5.0133, upto 4 places of decimals.

Concept: Binomial Theorem for Negative Index Or Fraction
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.4 | Q 4. (ii) | Page 82
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