Question

toe binomial theorem to evaluate the following
upto four places of decimals.
√99​

Answer 1

Answer:

root 99 can be written as 99.000000 and now divide it by the division square method

Answer 2

√99 upto four places of decimals is 9.9498

we have to find value of √99 using binomial expansion.

we know from binomial expansion,

(1 ± x)ⁿ = 1 ± nx + n(n - 1)x²/2! ± n(n - 1)(n - 2)/3! + .......... ∞

here, √99 = √(100 - 1)

= (100 - 1)½

= [100(1 - 1/100)]½

= [(100)½ (1 - 0.01)½]

= 10(1 - 0.01)½

now here we have seen (1 - 0.01)½ is similar to (1 - x)ⁿ

so, using formula, (1 - x)ⁿ = 1 - nx + n(n - 1)x²/2! - n(n - 1)(n - 2)x³/3! + ..... ∞

so, (1 - 0.01)½ = 1 - 0.01/2 + 1/2(-1/2)(0.01)²/2 - (1/2)(-1/2)(-3/2)(0.01)³/6

= 1 - 0.005 - (0.0001)/8 - (0.000001)/48 + ....

= 0.994987...

now 10(0.994987....) = 9.94987...

so, √99 upto four places of decimals is 9.9498

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