how to calculate cube root without using prime factorization? and how to calculate ³√60? or something else that has a decimal re

Question

2 years ago

5

sult?

1 answer:

Marat540 [252] · Answer 1 · 2023-07-17T12:03:25+03:00

The cube root of 60 is 3.87 approximately.

Step by step solution:

We can calculate the cube root by Halley's method:

The formula is $\sqrt[3]{a} = x ((x^{3} + 2a)/(2x^{3} + a))$

where,

a = number whose cube root is being calculated

x = integer guess of its cube root.

Here a = 60,

Suppose x as 3

[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 60]

⇒ x = 3

Therefore,

∛60 = 3 (3³ + 2 × 60)/(2 × 3³ + 60)) = 3.87

⇒ ∛60 ≈ 3.87

Therefore, the cube root of 60 is 3.87 approximately.

Here , ∛60 is irrational because it cannot be expressed in the form of p/q where q ≠ 0.

Therefore, the value of the cube root of 60 is an irrational number.

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