The value of (997)1/3 according to binomial theorem is

The value of (997)^(¹/₃) according to binomial theorem is;

9.99

The value of

(997)^(¹/₃)

⇒ (1000 - 3)^(¹/₃)

Factorizing out common terms gives;

⇒ (1000)^(¹/₃) * (1 - 3/1000)^(¹/₃)

Using the given approximations from binomial theorem, we have;

⇒ 10(1 + (¹/₃ × -³/₁₀₀₀)

⇒ 10(1 - 0.001)

⇒ 10 × 0.999

⇒ 9.99

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9.99

Explanation:

The value of (997)^1/3

(997)^1/3

997 = (1000 - 3)

(1000 - 3)^1/3

Expanding :

[1000(1 - 3/1000)]^1/3

1000^1/3 * (1 - 3/1000)^1/3

Cube root of 1000

10 * (1 - 3/1000 * 1/3)

10 * (1 - 1/1000)

10 * (1 - 0.001)

10(0.999)

= 9.99

Hence, the value of (997)^1/3 according to binomial theorem is 9.99