Question

Calculate the given figure through binomial expression 1001^1/3

Answer 1

Answer:

Given, \bold{\sqrt[3]{1003}}

3

1003

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, \bold{\sqrt[3]{1003}}

3

1003

= 10.01