Cube Root of 256
The value of the cube root of 256 rounded to 6 decimal places is 6.349604. It is the real solution of the equation x3 = 256. The cube root of 256 is expressed as ∛256 or 4 ∛4 in the radical form and as (256)⅓ or (256)0.33 in the exponent form. The prime factorization of 256 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2, hence, the cube root of 256 in its lowest radical form is expressed as 4 ∛4.
- Cube root of 256: 6.349604208
- Cube root of 256 in Exponential Form: (256)⅓
- Cube root of 256 in Radical Form: ∛256 or 4 ∛4
1. | What is the Cube Root of 256? |
2. | How to Calculate the Cube Root of 256? |
3. | Is the Cube Root of 256 Irrational? |
4. | FAQs on Cube Root of 256 |
What is the Cube Root of 256?
The cube root of 256 is the number which when multiplied by itself three times gives the product as 256. Since 256 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Therefore, the cube root of 256 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = 6.3496.
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How to Calculate the Value of the Cube Root of 256?
Cube Root of 256 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 = 256
Let us assume x as 6
[∵ 63 = 216 and 216 is the nearest perfect cube that is less than 256]
⇒ x = 6
Therefore,
∛256 = 6 (63 + 2 × 256)/(2 × 63 + 256)) = 6.35
⇒ ∛256 ≈ 6.35
Therefore, the cube root of 256 is 6.35 approximately.
Is the Cube Root of 256 Irrational?
Yes, because ∛256 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = 4 ∛4 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 256 is an irrational number.
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Cube Root of 256 Solved Examples
-
Example 1: Given the volume of a cube is 256 in3. Find the length of the side of the cube.
Solution:
Volume of the Cube = 256 in3 = a3
⇒ a3 = 256
Cube rooting on both sides,
⇒ a = ∛256 in
Since the cube root of 256 is 6.35, therefore, the length of the side of the cube is 6.35 in. -
Example 2: What is the value of ∛256 + ∛(-256)?
Solution:
The cube root of -256 is equal to the negative of the cube root of 256.
i.e. ∛-256 = -∛256
Therefore, ∛256 + ∛(-256) = ∛256 - ∛256 = 0
-
Example 3: The volume of a spherical ball is 256π in3. What is the radius of this ball?
Solution:
Volume of the spherical ball = 256π in3
= 4/3 × π × R3
⇒ R3 = 3/4 × 256
⇒ R = ∛(3/4 × 256) = ∛(3/4) × ∛256 = 0.90856 × 6.3496 (∵ ∛(3/4) = 0.90856 and ∛256 = 6.3496)
⇒ R = 5.76899 in3
FAQs on Cube Root of 256
What is the Value of the Cube Root of 256?
We can express 256 as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 i.e. ∛256 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = 6.3496. Therefore, the value of the cube root of 256 is 6.3496.
What is the Cube of the Cube Root of 256?
The cube of the cube root of 256 is the number 256 itself i.e. (∛256)3 = (2561/3)3 = 256.
What is the Cube Root of -256?
The cube root of -256 is equal to the negative of the cube root of 256. Therefore, ∛-256 = -(∛256) = -(6.35) = -6.35.
If the Cube Root of 256 is 6.35, Find the Value of ∛0.256.
Let us represent ∛0.256 in p/q form i.e. ∛(256/1000) = 6.35/10 = 0.63. Hence, the value of ∛0.256 = 0.63.
Is 256 a Perfect Cube?
The number 256 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 256 is irrational, hence 256 is not a perfect cube.
How to Simplify the Cube Root of 256/343?
We know that the cube root of 256 is 6.3496 and the cube root of 343 is 7. Therefore, ∛(256/343) = (∛256)/(∛343) = 6.35/7 = 0.9071.
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