(1001)1/3 binomial expansion
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Given,
We know, according to Binomial theorem,
if Any number in the form of (1 + a)ⁿ , where a << 1
Then, (1 + a)ⁿ ≈ 1 + na
Now, (1003)⅓ = (1000 + 3)⅓
= (1000)⅓[ 1 + 3/1000]⅓
= 10[1 + 0.003]⅓
∵ 0.003 << 1
so, 10(1 + 0.003)⅓ = 10(1 + 0.003 × 1/3) = 10(1 + 0.001)
= 10 × 1.001
= 10.01
Hence, = 10.1
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