Question

Find the value of (1001)^⅓ .

Answer 1

We know ,
according to binomial expansion ,
( x ± a)ⁿ
= xⁿ ( 1 + a/x)ⁿ
= xⁿ( 1 + na/x)

where x >>a

now,
( 1001)⅓ = ( 1000 +1)⅓

= (1000)⅓{ 1 + 1/1000)⅓

= (10)³×⅓ { 1 + 1/1000)⅓

= 10 { 1 + 1/1000}⅓

we know , 1 >> 1/1000
hence,

= 10( 1 + 1/1000)⅓ = 10{1 +1/3 × 1/1000}

= 10 { 1 + 1/3000}

= 10 × 1.00033
=10.0033