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Cube Root of 26

The value of the cube root of 26 rounded to 5 decimal places is 2.9625. It is the real solution of the equation x³ = 26. The cube root of 26 is expressed as ∛26 in the radical form and as (26)^⅓ or (26)^0.33 in the exponent form. The prime factorization of 26 is 2 × 13, hence, the cube root of 26 in its lowest radical form is expressed as ∛26.

Cube root of 26: 2.962496068
Cube root of 26 in Exponential Form: (26)^⅓
Cube root of 26 in Radical Form: ∛26

Cube Root of 26

1.	What is the Cube Root of 26?
2.	How to Calculate the Cube Root of 26?
3.	Is the Cube Root of 26 Irrational?
4.	FAQs on Cube Root of 26

What is the Cube Root of 26?

The cube root of 26 is the number which when multiplied by itself three times gives the product as 26. Since 26 can be expressed as 2 × 13. Therefore, the cube root of 26 = ∛(2 × 13) = 2.9625.

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How to Calculate the Value of the Cube Root of 26?

Cube Root of 26 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 = 26
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 26]
⇒ x = 2
Therefore,
∛26 = 2 (2³ + 2 × 26)/(2 × 2³ + 26)) = 2.86
⇒ ∛26 ≈ 2.86
Therefore, the cube root of 26 is 2.86 approximately.

Is the Cube Root of 26 Irrational?

Yes, because ∛26 = ∛(2 × 13) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 26 is an irrational number.

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Cube Root of 26 Solved Examples

Example 1: Given the volume of a cube is 26 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 26 in³ = a³
⇒ a³ = 26
Cube rooting on both sides,
⇒ a = ∛26 in
Since the cube root of 26 is 2.96, therefore, the length of the side of the cube is 2.96 in.
Example 2: The volume of a spherical ball is 26π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 26π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 26
⇒ R = ∛(3/4 × 26) = ∛(3/4) × ∛26 = 0.90856 × 2.9625 (∵ ∛(3/4) = 0.90856 and ∛26 = 2.9625)
⇒ R = 2.69161 in³
Example 3: Find the real root of the equation x³ − 26 = 0.

Solution:

x³ − 26 = 0 i.e. x³ = 26
Solving for x gives us,
x = ∛26, x = ∛26 × (-1 + √3i))/2 and x = ∛26 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛26
Therefore, the real root of the equation x³ − 26 = 0 is for x = ∛26 = 2.9625.

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FAQs on Cube Root of 26

What is the Value of the Cube Root of 26?

We can express 26 as 2 × 13 i.e. ∛26 = ∛(2 × 13) = 2.9625. Therefore, the value of the cube root of 26 is 2.9625.

What is the Cube Root of -26?

The cube root of -26 is equal to the negative of the cube root of 26. Therefore, ∛-26 = -(∛26) = -(2.962) = -2.962.

What is the Value of 3 Plus 12 Cube Root 26?

The value of ∛26 is 2.962. So, 3 + 12 × ∛26 = 3 + 12 × 2.962 = 38.544000000000004. Hence, the value of 3 plus 12 cube root 26 is 38.544000000000004.

Is 26 a Perfect Cube?

The number 26 on prime factorization gives 2 × 13. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 26 is irrational, hence 26 is not a perfect cube.

What is the Cube of the Cube Root of 26?

The cube of the cube root of 26 is the number 26 itself i.e. (∛26)³ = (26^1/3)³ = 26.

If the Cube Root of 26 is 2.96, Find the Value of ∛0.026.

Let us represent ∛0.026 in p/q form i.e. ∛(26/1000) = 2.96/10 = 0.3. Hence, the value of ∛0.026 = 0.3.

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