Find the value using cube-root table (correct to three decimal places) ³√31/³√64
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Answers
Step-by-step explanation:
3√31/3√64=
ans 0.695970545
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Cube Root of 31
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The value of the cube root of 31 rounded to 5 decimal places is 3.14138. It is the real solution of the equation x3 = 31. The cube root of 31 is expressed as ∛31 in the radical form and as (31)⅓ or (31)0.33 in the exponent form. The prime factorization of 31 is 31, hence, the cube root of 31 in its lowest radical form is expressed as ∛31.
Cube root of 31: 3.141380652
Cube root of 31 in Exponential Form: (31)⅓
Cube root of 31 in Radical Form: ∛31
Cube Root of 31
What is the Cube Root of 31?
The cube root of 31 is the number which when multiplied by itself three times gives the product as 31. The number 31 is prime. Therefore, the cube root of 31 = ∛31 = 3.1414.Its formula is ∛a ≈ x ((x3 + 2a)/(2x3 + a))
where,
a = number whose cube root is being calculated
x = integer guess of its cube root.
Here a = 31
Let us assume x as 3
[∵ 33 = 27 and 27 is the nearest perfect cube that is less than 31]
⇒ x = 3
Therefore,
∛31 = 3 (33 + 2 × 31)/(2 × 33 + 31)) = 3.14
⇒ ∛31 ≈ 3.14
Therefore, the cube root of 31 is 3.14 approximately.
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