Cube Root of 1728

Cube Root of 1728 is 12. Cube root of a number is a value that, when multiplied by itself twice (or cubed), results in the original number. For 1728, as 12 × 12 × 12 = 1728, indicating that 12 raised to the power of 3 equals 1728. Therefore, the cube root of 1728 is 12. In this article, we will learn in detail about Cube Root of 1728, and how to find it using different methods.

What is the Cube Root?

Cube root of a number is the value that, when multiplied by itself twice (or cubed), results in the original number. Mathematically, if x is a real number, the cube root of x is denoted as ∛x​, and it satisfies the equation:

(∛x)³ = x

For example, the cube root of 8 is 2 because 2 × 2 × 2 = 8. Similarly, the cube root of 27 is 3 because 3 × 3 × 3 = 27.

Cube Root of 1728

The cube root of 1728, denoted as ∛1728, is the number that, when multiplied by itself twice, results in 1728.

The cube root of 1728 is 12

Let’s explore the methods to determine this cube root and the significance behind it.

Cube Root of 1728 Calculator

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

We can calculate cube root of 1728 using following two methods:

• Prime Factorization Method

Learn, Cube and Cube Roots

Cube Root of 1728 by Prime Factorization

Step 1: Prime Factorization of 1728

Thus, prime factorization of 1728 is 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3.

Step 2: Group the common factors in the pair of three i.e.,

• 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3)

Step 3: Multiply one factor from each group to find the cube root.

Thus, cube root of 1728 = 2 × 2 × 3 = 12.

Facts about 1728

Some of the interesting facts about 1728 are:

• 1728 is the cube of 12.
• It is the product of the six divisors of 12 (1, 2, 3, 4, 6, 12).
• It is the product of the first four composite numbers (4, 6, 8, and 9).
• 1728 can be expressed as 1728 = 3³ × 4³ = 2³ × 6³ = 12³.
• 1728 can be also be expressed as 1728 = 6³ + 8³ + 10³
• It has 28 divisors.

Is the Cube Root of 1728 a Rational or Irrational Number?

The cube root of 1728 is a rational number. This is because 1728 is a perfect cube, specifically 12³. Rational numbers are defined as numbers that can be expressed as the ratio of two integers. Since 1728 is the cube of the rational number 12, its cube root, which is 12, is also a rational number.

Read More,

• Cubes 1 to 20
• Squares and Cubes
• Perfect Cube of Numbers
• Cubes 1 to 30
• Cube root of a number

Cube Root of 1728 FAQs

What is the Cube Root of 1728?

The cube root of 1728 is 12.

Why is 1728 a Special Number?

1728 is special as it is the cube of 12 and has unique mathematical properties.

Can Cube Roots be Negative?

No, cube roots of real numbers can only be negative if the original number is negative.

Are There Multiple Cube Roots for a Number?

Yes, every real number has one real cube root, but complex numbers introduce additional roots.

Is the Cube Root of 1728 a Whole Number?

Yes, the cube root of 1728 is a whole number, specifically 12.