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Cube Root of 10000

The value of the cube root of 10000 rounded to 6 decimal places is 21.544347. It is the real solution of the equation x3 = 10000. The cube root of 10000 is expressed as ∛10000 or 10 ∛10 in the radical form and as (10000)⅓ or (10000)0.33 in the exponent form. The prime factorization of 10000 is 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5, hence, the cube root of 10000 in its lowest radical form is expressed as 10 ∛10.

  • Cube root of 10000: 21.5443469
  • Cube root of 10000 in Exponential Form: (10000)⅓
  • Cube root of 10000 in Radical Form: ∛10000 or 10 ∛10

Cube Root of 10000

1. What is the Cube Root of 10000?
2. How to Calculate the Cube Root of 10000?
3. Is the Cube Root of 10000 Irrational?
4. FAQs on Cube Root of 10000

What is the Cube Root of 10000?

The cube root of 10000 is the number which when multiplied by itself three times gives the product as 10000. Since 10000 can be expressed as 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5. Therefore, the cube root of 10000 = ∛(2 × 2 × 2 × 2 × 5 × 5 × 5 × 5) = 21.5443.

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How to Calculate the Value of the Cube Root of 10000?

Cube Root of 10000 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 = 10000
Let us assume x as 21
[∵ 213 = 9261 and 9261 is the nearest perfect cube that is less than 10000]
⇒ x = 21
Therefore,
∛10000 = 21 (213 + 2 × 10000)/(2 × 213 + 10000)) = 21.54
⇒ ∛10000 ≈ 21.54
Therefore, the cube root of 10000 is 21.54 approximately.

Is the Cube Root of 10000 Irrational?

Yes, because ∛10000 = ∛(2 × 2 × 2 × 2 × 5 × 5 × 5 × 5) = 10 ∛10 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 10000 is an irrational number.

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Cube Root of 10000 Solved Examples

  1. Example 1: What is the value of ∛10000 ÷ ∛(-10000)?

    Solution:

    The cube root of -10000 is equal to the negative of the cube root of 10000.
    ⇒ ∛-10000 = -∛10000

    Therefore,
    ⇒ ∛10000/∛(-10000) = ∛10000/(-∛10000) = -1

  2. Example 2: Find the real root of the equation x3 − 10000 = 0.

    Solution:

    x3 − 10000 = 0 i.e. x3 = 10000
    Solving for x gives us,
    x = ∛10000, x = ∛10000 × (-1 + √3i))/2 and x = ∛10000 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛10000
    Therefore, the real root of the equation x3 − 10000 = 0 is for x = ∛10000 = 21.5443.

  3. Example 3: Given the volume of a cube is 10000 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 10000 in3 = a3
    ⇒ a3 = 10000
    Cube rooting on both sides,
    ⇒ a = ∛10000 in
    Since the cube root of 10000 is 21.54, therefore, the length of the side of the cube is 21.54 in.

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FAQs on Cube Root of 10000

What is the Value of the Cube Root of 10000?

We can express 10000 as 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5 i.e. ∛10000 = ∛(2 × 2 × 2 × 2 × 5 × 5 × 5 × 5) = 21.54435. Therefore, the value of the cube root of 10000 is 21.54435.

What is the Cube Root of -10000?

The cube root of -10000 is equal to the negative of the cube root of 10000. Therefore, ∛-10000 = -(∛10000) = -(21.544) = -21.544.

What is the Cube of the Cube Root of 10000?

The cube of the cube root of 10000 is the number 10000 itself i.e. (∛10000)3 = (100001/3)3 = 10000.

How to Simplify the Cube Root of 10000/125?

We know that the cube root of 10000 is 21.54435 and the cube root of 125 is 5. Therefore, ∛(10000/125) = (∛10000)/(∛125) = 21.544/5 = 4.3088.

What is the Value of 19 Plus 1 Cube Root 10000?

The value of ∛10000 is 21.544. So, 19 + 1 × ∛10000 = 19 + 1 × 21.544 = 40.544. Hence, the value of 19 plus 1 cube root 10000 is 40.544.

If the Cube Root of 10000 is 21.54, Find the Value of ∛10.

Let us represent ∛10.0 in p/q form i.e. ∛(10000/1000) = 21.54/10 = 2.15. Hence, the value of ∛10.0 = 2.15.

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