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What is the largest perfect cube factor of 54

Sagot :

peunice882

Cube Root of 54

The value of the cube root of 54 rounded to 7 decimal places is 3.7797631. It is the real solution of the equation x3 = 54. The cube root of 54 is expressed as ∛54 or 3 ∛2 in the radical form and as (54)⅓ or (54)0.33 in the exponent form. The prime factorization of 54 is 2 × 3 × 3 × 3, hence, the cube root of 54 in its lowest radical form is expressed as 3 ∛2.

Cube root of 54: 3.77976315

Cube root of 54 in Exponential Form: (54)⅓

Cube root of 54 in Radical Form: ∛54 or 3 ∛2

Cube Root of 54

What is the Cube Root of 54?

The cube root of 54 is the number which when multiplied by itself three times gives the product as 54. Since 54 can be expressed as 2 × 3 × 3 × 3. Therefore, the cube root of 54 = ∛(2 × 3 × 3 × 3) = 3.7798.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 54?

Cube Root of 54 by Halley's Method

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 = 54

Let us assume x as 3

[∵ 33 = 27 and 27 is the nearest perfect cube that is less than 54]

⇒ x = 3

Therefore,

∛54 = 3 (33 + 2 × 54)/(2 × 33 + 54)) = 3.75

⇒ ∛54 ≈ 3.75

Therefore, the cube root of 54 is 3.75 approximately.

Is the Cube Root of 54 Irrational?

Yes, because ∛54 = ∛(2 × 3 × 3 × 3) = 3 ∛2 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 54 is an irrational number.

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