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Use binomial theorem to evaluate the following upto four places of decimal 99 - Mathematics and Statistics

Sum

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

`sqrt(99)`

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Solution

`sqrt(99) = (99)^(1/2)`

= `(100 - 1)^(1/2)`

= `[100(1 - 1/100)]^(1/2)`

= `(100)^(1/2) (1 - 0.01)^(1/2)`

= `10[1 - 1/2(0.01) + (1/2(1/2 - 1))/(2!) (0.01)^2 - ......]`

= `10[1 - 1/2(0.01) + (1/2((-1)/2))/2 (0.01)^2 - ......]`

= `10[1 - 0.005 - (0.0001)/8 - ......]`

= 10 [1 – 0.005 – 0.0000125 – ……]

= 10 [0.9949875]

= 9.949875

= 9.9499

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. (i) | Page 82
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