Cube Root of 100 - How to Find the Cube Root of 100? [Solved] (2024)

The value of the cube root of 100 rounded to 6 decimal places is 4.641589. It is the real solution of the equation x³ = 100. The cube root of 100 is expressed as ∛100 in the radical form and as (100)^⅓ or (100)^0.33 in the exponent form. The prime factorization of 100 is 2 × 2 × 5 × 5, hence, the cube root of 100 in its lowest radical form is expressed as ∛100.

Cube root of 100: 4.641588834
Cube root of 100 in Exponential Form: (100)^⅓
Cube root of 100 in Radical Form: ∛100

1.	What is the Cube Root of 100?
2.	How to Calculate the Cube Root of 100?
3.	Is the Cube Root of 100 Irrational?
4.	FAQs on Cube Root of 100

What is the Cube Root of 100?

The cube root of 100 is the number which when multiplied by itself three times gives the product as 100. Since 100 can be expressed as 2 × 2 × 5 × 5. Therefore, the cube root of 100 = ∛(2 × 2 × 5 × 5) = 4.6416.

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How to Calculate the Value of the Cube Root of 100?

Cube Root of 100 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 = 100
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 100]
⇒ x = 4
Therefore,
∛100 = 4 (4³ + 2 × 100)/(2 × 4³ + 100)) = 4.63
⇒ ∛100 ≈ 4.63
Therefore, the cube root of 100 is 4.63 approximately.

Is the Cube Root of 100 Irrational?

Yes, because ∛100 = ∛(2 × 2 × 5 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 100 is an irrational number.

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Cube Root of 343

Cube Root of 100 Solved Examples

Example 1: What is the value of ∛100 + ∛(-100)?
Solution:
The cube root of -100 is equal to the negative of the cube root of 100.
i.e. ∛-100 = -∛100
See Also
Cube Root of a Number | How to Find the Cube Root of a Number?
Therefore, ∛100 + ∛(-100) = ∛100 - ∛100 = 0
Example 2: Given the volume of a cube is 100 in³. Find the length of the side of the cube.
Solution:
Volume of the Cube = 100 in³ = a³
⇒ a³ = 100
Cube rooting on both sides,
⇒ a = ∛100 in
Since the cube root of 100 is 4.64, therefore, the length of the side of the cube is 4.64 in.
Example 3: The volume of a spherical ball is 100π in³. What is the radius of this ball?
Solution:
Volume of the spherical ball = 100π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 100
⇒ R = ∛(3/4 × 100) = ∛(3/4) × ∛100 = 0.90856 × 4.64159 (∵ ∛(3/4) = 0.90856 and ∛100 = 4.64159)
⇒ R = 4.21716 in³

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FAQs on Cube Root of 100

What is the Value of the Cube Root of 100?

We can express 100 as 2 × 2 × 5 × 5 i.e. ∛100 = ∛(2 × 2 × 5 × 5) = 4.64159. Therefore, the value of the cube root of 100 is 4.64159.

What is the Cube Root of -100?

The cube root of -100 is equal to the negative of the cube root of 100. Therefore, ∛-100 = -(∛100) = -(4.642) = -4.642.

If the Cube Root of 100 is 4.64, Find the Value of ∛0.1.

Let us represent ∛0.1 in p/q form i.e. ∛(100/1000) = 4.64/10 = 0.46. Hence, the value of ∛0.1 = 0.46.

Is 100 a Perfect Cube?

The number 100 on prime factorization gives 2 × 2 × 5 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 100 is irrational, hence 100 is not a perfect cube.

How to Simplify the Cube Root of 100/343?

We know that the cube root of 100 is 4.64159 and the cube root of 343 is 7. Therefore, ∛(100/343) = (∛100)/(∛343) = 4.642/7 = 0.6631.

What is the Cube of the Cube Root of 100?

The cube of the cube root of 100 is the number 100 itself i.e. (∛100)³ = (100^1/3)³ = 100.

FAQs

Cube Root of 100 - How to Find the Cube Root of 100? [Solved]? ›

What is the Cube Root of 100? The cube root of 100 is the number which when multiplied by itself three times gives the product as 100. Since 100 can be expressed as 2 × 2 × 5 × 5. Therefore, the cube root of 100 = ∛(2 × 2 × 5 × 5) = 4.6416.

How to solve for cube root? ›

It can be calculated by first finding out the prime factorization of the given number and then later applying the cube root formula. Suppose, x is any number such that, x = y × y × y. The formula to calculate the cube root is given as: Cube root of x = ∛x = ∛(y × y × y) = y.

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What is a perfect cube up to 100? ›

So we can say that the positive integers whose cubes are 100 or below are 1, 2, 3 and 4 only. Thus there are 4 perfect cubes from 1 to 100 and they are 1, 8, 27 and 64. Thus there are 4 perfect cubes from -100 to -1. They are -1, -8, -27 and -64.

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How to solve the cube root of 100? ›

What is the Value of the Cube Root of 100? We can express 100 as 2 × 2 × 5 × 5 i.e. ∛100 = ∛(2 × 2 × 5 × 5) = 4.64159. Therefore, the value of the cube root of 100 is 4.64159.

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How to find cube root short trick? ›

Tricks to find Cube Root: Vedic Maths

To find the unit place of the cube root always remember the following points: • ...
Now, strike off the last 3 digits of the given number.
Now, find the nearest cube of the first 2 digit from the left, i.e., 39. The nearest cube is 27.
Now, 3 is the cube root of 27.

Jan 25, 2018

What number is √ 100? ›

We already found that √100 = 10. The number 10 is a rational number. So, the square root of 100 is a rational number.

Read On ›

What is the value of 100 √? ›

The value of √100 is 10 because 102 = 100. √100 represents the square root of 100. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, 10 multiplied by itself is 100, so the value of √100 is 10.

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How to find cube root calculator? ›

If your calculator doesn't have a cube root button, you can use the exponentiation button (usually marked as "^") and enter the fraction 1/3. 3. Press the "=" button to get the result. For example, to find the cube root of 8, you would enter "8", press the "∛" button (or "^" and then "1/3"), and then press "=".

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Will the cube of 100 have zeros? ›

Cube of 100 is 1000000. So 6 zeroes.

Is 100 a cube number? ›

The square numbers up to 100 are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. A cube number is a number multiplied by itself 3 times. The cube numbers up to 100 are 1, 8, 27, and 64. Cube numbers can be depicted as three-dimensional cubes.

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How to find perfect cube root? ›

Cube root of a number can be found by a very simple method which is the prime factorization method. Cube root is denoted by '∛ ' symbol. Example: ∛8 = ∛(2 × 2 × 2) = 2. Since, 8 is a perfect cube number, it is easy to find the cube root of a number.

What is the formula for the cube root function? ›

What is the Formula of Cube Root Function? The formula for basic (parent) cube root function is f(x) = ∛x. It can also be of the form f(x) = a ∛(bx - h) + k after the transformations. Here, a, b, h, and k are real numbers and they represent the transformations.

Keep Reading ›

How to find the value of 3 √ 3? ›

Divide 3 by 1.4. Step 4: Again, divide this value by 1.4. Step 5: Now, take the average of 1.4, 1.4 and 1.53 to get a value of ³√3. The actual value of ³√3 is 1.442249.

How to calculate the cube root of 729? ›

What is the Value of the Cube Root of 729? We can express 729 as 3 × 3 × 3 × 3 × 3 × 3 i.e. ∛729 = ∛(3 × 3 × 3 × 3 × 3 × 3) = 9. Therefore, the value of the cube root of 729 is 9.

What is the rule for cube root? ›

Cube root of number is a value which when multiplied by itself thrice or three times produces the original value. For example, the cube root of 27, denoted as ³√27, is 3, because when we multiply 3 by itself three times we get 3 x 3 x 3 = 27 = 3³.

Find Out More ›