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binomial theoram — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSbinomial theoram1 Mark
MCQ
Cube root of $217$ is
  • ✓
    $6.01$
  • B
    $6.04$
  • C
    $6.02$
  • D
    None of these
✓

Answer

Correct option: A.
$6.01$
a
(a) ${(217)^{1/3}} = {({6^3} + 1)^{1/3}} = 6{\left( {1 + \frac{1}{{{6^3}}}} \right)^{1/3}}$

On expansion by binomial theorem

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

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