Question

$find \: the \: value \: of \: {(1003)}^{ \frac{1}{3} } according \: \\ to \: binomial \: theorem.$


##No spammed answer please##

Answer 1

Hey !!!

(1003 )^1/3

3√1003 = (1000 + 3 ))^1/2

=> 1000^1/3 [1 + 3/1000] ^1/3

=> 3√1000 [1 + 3/1000]^1/3

=> 10[1 + 3/1000×1/3]

°•° in binomial Approximations , we know that x is very very small /1 or , x <<<<<<1

then ,( 1 + x )^n = [1+nx]

since , 10[1 +1/1000]

=> 10[1 + 0.001 ]

=> 10[1.001 ]

=> 10.01 Answer ..
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you can verify it ✔

(10.01 )³ = 1003.

1003 ≌1003.003001

hence, 1003 =1003

here approximately, RHS =LHS prooved

hence , our answer is 10.01 ✌

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Hope it helps you !!!

@Rajukumar111