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Cube Root of 700

The value of the cube root of 700 rounded to 5 decimal places is 8.87904. It is the real solution of the equation x³ = 700. The cube root of 700 is expressed as ∛700 in the radical form and as (700)^⅓ or (700)^0.33 in the exponent form. The prime factorization of 700 is 2 × 2 × 5 × 5 × 7, hence, the cube root of 700 in its lowest radical form is expressed as ∛700.

Cube root of 700: 8.879040017
Cube root of 700 in Exponential Form: (700)^⅓
Cube root of 700 in Radical Form: ∛700

Cube Root of 700

1.	What is the Cube Root of 700?
2.	How to Calculate the Cube Root of 700?
3.	Is the Cube Root of 700 Irrational?
4.	FAQs on Cube Root of 700

What is the Cube Root of 700?

The cube root of 700 is the number which when multiplied by itself three times gives the product as 700. Since 700 can be expressed as 2 × 2 × 5 × 5 × 7. Therefore, the cube root of 700 = ∛(2 × 2 × 5 × 5 × 7) = 8.879.

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How to Calculate the Value of the Cube Root of 700?

Cube Root of 700 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 = 700
Let us assume x as 8
[∵ 8³ = 512 and 512 is the nearest perfect cube that is less than 700]
⇒ x = 8
Therefore,
∛700 = 8 (8³ + 2 × 700)/(2 × 8³ + 700)) = 8.87
⇒ ∛700 ≈ 8.87
Therefore, the cube root of 700 is 8.87 approximately.

Is the Cube Root of 700 Irrational?

Yes, because ∛700 = ∛(2 × 2 × 5 × 5 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 700 is an irrational number.

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Cube Root of 700 Solved Examples

Example 1: Given the volume of a cube is 700 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 700 in³ = a³
⇒ a³ = 700
Cube rooting on both sides,
⇒ a = ∛700 in
Since the cube root of 700 is 8.88, therefore, the length of the side of the cube is 8.88 in.
Example 2: The volume of a spherical ball is 700π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 700π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 700
⇒ R = ∛(3/4 × 700) = ∛(3/4) × ∛700 = 0.90856 × 8.87904 (∵ ∛(3/4) = 0.90856 and ∛700 = 8.87904)
⇒ R = 8.06714 in³
Example 3: Find the real root of the equation x³ − 700 = 0.

Solution:

x³ − 700 = 0 i.e. x³ = 700
Solving for x gives us,
x = ∛700, x = ∛700 × (-1 + √3i))/2 and x = ∛700 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛700
Therefore, the real root of the equation x³ − 700 = 0 is for x = ∛700 = 8.879.

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FAQs on Cube Root of 700

What is the Value of the Cube Root of 700?

We can express 700 as 2 × 2 × 5 × 5 × 7 i.e. ∛700 = ∛(2 × 2 × 5 × 5 × 7) = 8.87904. Therefore, the value of the cube root of 700 is 8.87904.

Why is the Value of the Cube Root of 700 Irrational?

The value of the cube root of 700 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛700 is irrational.

How to Simplify the Cube Root of 700/343?

We know that the cube root of 700 is 8.87904 and the cube root of 343 is 7. Therefore, ∛(700/343) = (∛700)/(∛343) = 8.879/7 = 1.2684.

Is 700 a Perfect Cube?

The number 700 on prime factorization gives 2 × 2 × 5 × 5 × 7. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 700 is irrational, hence 700 is not a perfect cube.

What is the Cube of the Cube Root of 700?

The cube of the cube root of 700 is the number 700 itself i.e. (∛700)³ = (700^1/3)³ = 700.

If the Cube Root of 700 is 8.88, Find the Value of ∛0.7.

Let us represent ∛0.7 in p/q form i.e. ∛(700/1000) = 8.88/10 = 0.89. Hence, the value of ∛0.7 = 0.89.

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