Question

Solve (999)^1/3 using binomial theorem
It's urgent...please

Answer 1

Answer:

we know ,

according to binomial expansion ,

( x ± a)ⁿ

= xⁿ ( 1 + a/x)ⁿ

= xⁿ( 1 + na/x)

where x >>a

now,

( 999)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 × 0.99666

=9.9666