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प्रश्न
Use binomial theorem to evaluate the following upto four places of decimal
`root(4)(16.08)`
उत्तर
`root(4)(16.08)`
= `(16 + 0.08)^(1/4)`
= `[16(1 + 0.005)]^(1/4)`
= `16^(1/4) (1 + 0.005)^(1/4)`
= `2[1 + 1/4 (0.005) + (1/4(1/4 - 1))/(2!) (0.005)^2 + ......]`
= `2[1 + 1/4 (0.005) + (1/4((-3)/4))/(2) (0.005)^2 + ......]`
= `2[1 + 0.00125 - (0.000075)/32 + ......]`
= 2 [1 + 0.00125 – 0.0000023 + ……]
= 2 (1.0012477)
= 2.0024954
= 2.0025
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