A day full of math games & activities. Find one near you.

Cube Root of 1728

The value of the cube root of 1728 is 12. It is the real solution of the equation x³ = 1728. The cube root of 1728 is expressed as ∛1728 in radical form and as (1728)^⅓ or (1728)^0.33 in the exponent form. As the cube root of 1728 is a whole number, 1728 is a perfect cube.

Cube root of 1728: 12
Cube root of 1728 in exponential form: (1728)^⅓
Cube root of 1728 in radical form: ∛1728

Cube Root of 1728

1.	What is the Cube Root of 1728?
2.	How to Calculate the Cube Root of 1728?
3.	Is the Cube Root of 1728 Irrational?
4.	FAQs on Cube Root of 1728

What is the Cube Root of 1728?

The cube root of 1728 is the number which when multiplied by itself three times gives the product as 1728. Since 1728 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3. Therefore, the cube root of 1728 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 12.

How to Calculate the Value of the Cube Root of 1728?

Cube Root of 1728 by Prime Factorization

Prime factorization of 1728 is 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
Simplifying the above expression: 2⁶ × 3³
Simplifying further: 12³

Therefore, the cube root of 1728 by prime factorization is (2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3)^1/3 = 12.

Is the Cube Root of 1728 Irrational?

No, because ∛1728 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) can be expressed in the form of p/q i.e. 12/1. Therefore, the value of the cube root of 1728 is an integer (rational).

☛ Also Check:

Cube Root of 1728 Solved Examples

Example 1: The volume of a spherical ball is 1728π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 1728π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 1728
⇒ R = ∛(3/4 × 1728) = ∛(3/4) × ∛1728 = 0.90856 × 12 (∵ ∛(3/4) = 0.90856 and ∛1728 = 12)
⇒ R = 10.90272 in³
Example 2: What is the value of ∛1728 ÷ ∛(-1728)?

Solution:

The cube root of -1728 is equal to the negative of the cube root of 1728.
⇒ ∛-1728 = -∛1728

Therefore,
⇒ ∛1728/∛(-1728) = ∛1728/(-∛1728) = -1
Example 3: Find the real root of the equation x³ − 1728 = 0.

Solution:

x³ − 1728 = 0 i.e. x³ = 1728
Solving for x gives us,
x = ∛1728, x = ∛1728 × (-1 + √3i))/2 and x = ∛1728 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛1728
Therefore, the real root of the equation x³ − 1728 = 0 is for x = ∛1728 = 12.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on Cube Root of 1728

What is the Value of the Cube Root of 1728?

We can express 1728 as 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 i.e. ∛1728 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 12. Therefore, the value of the cube root of 1728 is 12.

Is 1728 a Perfect Cube?

The number 1728 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3. On combining the prime factors in groups of 3 gives 12. So, the cube root of 1728 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 12 (perfect cube).

If the Cube Root of 1728 is 12, Find the Value of ∛1.728.

Let us represent ∛1.728 in p/q form i.e. ∛(1728/1000) = 12/10 = 1.2. Hence, the value of ∛1.728 = 1.2.

What is the Cube of the Cube Root of 1728?

The cube of the cube root of 1728 is the number 1728 itself i.e. (∛1728)³ = (1728^1/3)³ = 1728.

What is the Value of 14 Plus 20 Cube Root 1728?

The value of ∛1728 is 12. So, 14 + 20 × ∛1728 = 14 + 20 × 12 = 254. Hence, the value of 14 plus 20 cube root 1728 is 254.

Why is the value of the Cube Root of 1728 Rational?

The value of the cube root of 1728 can be expressed in the form of p/q i.e. = 12/1, where q ≠ 0. Therefore, the ∛1728 is rational.

Math worksheets and
visual curriculum