The approximate value of 7-9951-3 correct to four decimal places is

The correct option is A 1.9995 (7.995)^1/3 = (8 0.005)^1/3 = (8)^ 1/3 [1 0.005/8]^ 1/3 = 2[1 1/3 × 0.005/8 + 1/3( 1/3 1)/2 + 1 (0.005/8)^2 + ...... ...

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Standard XII

Mathematics

Binomial Expression

The approxima...

Question

The approximate value of $(7.995)^{\frac{1}{3}}$ correct to four decimal places is

1.9995

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1.9996

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1.9990

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1.9991

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Solution

The correct option is A
1.9995

$(7.995)^{\frac{1}{3}}$ = $(8 - 0.005)^{\frac{1}{3}}$ = $(8)^{\frac{1}{3}}$ $[1 - \frac{0.005}{8}]^{\frac{1}{3}}$

= 2[1 - $\frac{1}{3}$ × $\frac{0.005}{8}$ + $\frac{\frac{1}{3} (\frac{1}{3} - 1)}{2 + 1}$ $(\frac{0.005}{8})^{2}$ + ............]

= 2[1 - $\frac{0.005}{24}$ - $\frac{\frac{1}{3} \times \frac{1}{3}}{1}$ × $\frac{(0.005)^2}{8} + ......... ]$

$= 2 (1 - 0.000208) = 2 \times 0.999792 = 1.9995$

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The approximate value of (7.995)13 correct to four decimal places is

The correct option is A 1.9995 (7.995)13 = (8−0.005)13 = (8)13 [1−0.0058]13 = 2[1 - 13 × 0.0058 + 13(13−1)2+1 (0.0058)2 + ............] = 2[1 - 0.00524 - 13×131 × \(\frac{(0.005)^2}{8} + ......... ]\) =2(1−0.000208)=2×0.999792=1.9995

The approximate value of $(7.995)^{\frac{1}{3}}$ correct to four decimal places is