Cube root of 217 is Options: A . &nbsp 6.01 B . &nbsp 6.04 C . &nbsp 6.02 D . &nbsp None of these

Answer: Option A : A ( 217 ) 1 3 = ( 6 3 + 1 ) 1 3 = 6 ( 1 + 1 6 3 ) 1 3 On expansion by binomial theorem = 6 ( 1 + 1 3 × 216 − 1 × 2 3 × 3 × 2 ( 1 216 ) 2 + . . . . . . . . . ) = 6.01

Cube root of 217 is

Discussion Forum : Binomial Theorem

Question -

Cube root of 217 is

Options:

A . 6.01

B . 6.04

C . 6.02

D . None of these

Answer: Option A
:
A

$(217)^{\frac{1}{3}}$ = $(6^{3} + 1)^{\frac{1}{3}}$ = $6 (1 + \frac{1}{6^{3}})^{\frac{1}{3}}$

On expansion by binomial theorem

= $6 (1 + \frac{1}{3 \times 216} - \frac{1 \times 2}{3 \times 3 \times 2} (\frac{1}{216})^{2} + . . . . . . . . .)$ = 6.01

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