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Answer:
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
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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