The cube root of 217 is: | vedclass

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Question

(A) We need to find the value of $(217)^{1/3}$.We can write $217 = 216 + 1 = 6^3 + 1$.So,$(217)^{1/3} = (6^3 + 1)^{1/3} = 6(1 + \frac{1}{6^3})^{1/3}$.

Vedclass · Accepted Answer

$6.01$

Vedclass · Answer

(A) We need to find the value of $(217)^{1/3}$.We can write $217 = 216 + 1 = 6^3 + 1$.So,$(217)^{1/3} = (6^3 + 1)^{1/3} = 6(1 + \frac{1}{6^3})^{1/3}$.Using the binomial expansion $(1 + x)^n = 1 + nx + \frac{n(n-1)}{2!}x^2 + \dots$ for $|x| $(217)^{1/3} = 6 \left[ 1 + \frac{1}{3} \left( \frac{1}{216} ight) + \dots ight]$$= 6 + \frac{6}{3 	imes 216} = 6 + \frac{1}{108} \approx 6 + 0.009259 \approx 6.00926$.Rounding to two decimal places,we get $6.01$.Thus,the correct option is $A$.

The cube root of $217$ is:

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