Cube Root of 729

Cube Root of 729 is 9. The integer that returns the original value when multiplied by itself twice is known as the cube root. i.e. 9 when multiplied by itself twice gets 729, i.e. 9 × 9 × 9 = 729.

Therefore, The cube root of 729 is expressed as ∛729 in radical form and as (729)^1/3 or (729)^0.33 in the exponent form.

Cube Root Definition

A value that returns the original number after being multiplied twice by itself is known as the cube root of a number.

Some examples of cube root are:

• Cube root of 1: ∛1 = 1
• Cube root of 8: ∛8 = 2
• Cube root of 27: ∛27 = 3
• Cube root of -64: ∛(-64) = -4
• Cube root of 125: ∛125 = 5

What is Cube Root of 729?

The cube root of 729 is the number that can be multiplied by itself three times giving the product as 729. Therefore, 729 can be expressed as 3 × 3 × 3 × 3 × 3 × 3 or multiplying three times 9 both results in 729. Whereas, 729 is a perfect cube and the cube root of 729 is a whole number.

Value of Cube Root of 729

Mathematically, if Y is the cube root of 729, it can be represented as:

Y³ = 729,

⇒ Y = (729)^1/3

⇒ Y = 9

i.e. cube root of 729 is written as,

∛(729) = 9

Cube Root Calculator

You can find cube root of any number using the following cube root calculator:

How to Find Cube Root of 729?

To find the cube root of 729 various methods can be used that are given below:

• Successive Subtraction
• Prime Factorization Method

Cube Root of 729 by Successive Subtraction

As [Tex]\sum_{k=1}^{n} (k^3 – (k-1)^3) = \sum_{k=1}^{n} (3k^2 – 3k + 1) = n^3[/Tex].

Thus, subtracting successive difference of cubes i.e., 1, 7 , 19, 37, 61, 91, 127, 160, 217, . . . perfect cube numbers will always results in 0.

So Here, We have the following steps;

• 729-1=728
• 728-7=721
• 721-19=702
• 702-37=665
• 665-61=604
• 604-91=513
• 513-127=386
• 386-169=217
• 217-217=0

After performing, Successive Subtraction 9 times then we get 0.

Therefore, the cube root of 729 is 9.

Cube Root of 729 by Prime Factorization Method

Using the prime factorization method, the cube root of 729 can be found by following the steps that are given below;

Step 1: Start with the number 729

Step 2: Find prime factors of 729.

Thus, 729 = 3 × 3 × 3 × 3 × 3 × 3

Step 3: Now, Group three identical factors in one group. (3 × 3 × 3) × (3 × 3 × 3)

Step 4: Then take one factor from each group 3 and 3.

Step 5: Lastly, multiply the both factors 3 × 3 = 9.

Therefore, the cube root of 729 is 9.

Facts about 729

Some facts about 729 are:

• Prime Factorization: The prime factorization of 729 is 3⁶.
• Perfect Cube: 729 is a perfect cube, as it can be expressed as 9³.
• Square of a Square: 729 is the square of the square of 3, i.e., (3²)² = 9² = 729.
• Divisibility: Being a perfect cube, 729 is divisible by the cubes of smaller integers such as 1, 3, 9, 27, and 81.
• Pythagorean Triplet: 729 is part of a Pythagorean triplet (729, 2430, 2599).
• Arithmetic Progression: 729 can be expressed as the sum of consecutive odd numbers, starting from 1 up to 53.

Examples on Cube Root of 729

Example 1: Simplify ∛(729) × ∛(-729).

Solution:

We know,

• ∛(729) = 9
• ∛(-729) = -9

Hence, ∛(729) × ∛(-729) = 9 × (-9) = -81

Example 2: Simplify ∛(729) + ∛(-729).

Solution:

We know,

• ∛(729) = 9
• ∛(-729) = -9

Hence, ∛(729) + ∛(-729) = 9 + (-9) = 9 – 9 = 0

Example 3:  Find the value of 4 ∛(729)- 25.

Solution:

4 ∛(729) – 25

= 4 × 9 − 25

= 36 − 25

= 11

Therefore, 4 ∛(729) – 25 = 11.

Practice Questions

Q1: Calculate the Cube Root of (1/729).

Q2: Calculate the Cube Root of (-729).

Q3: Find Cube Root of,

• 8
• 27
• 35
• 810

Cube Root of 729: FAQs

What is the Value of the Cube Root of 729?

The cube root of 729 is 9.

Is the cube root of 729 a rational number?

Yes, the cube root of 729 is a rational number because it can be expressed in the form of two integers.

What is the cube root of 729 in radical form?

The cube root of 729 can be expressed as ∛ (729) in radical form.

What methods are used to find the cube root of 729?

For finding the cube root of 729, we use

• Successive Subtraction Method
• Prime Factorization Method

What is the cube root of negative 729?

The cube root of (-729) is (-9).

Is 729 a Perfect Cube?

Cube root of 729 is 9, which is a whole number, therefore, 729 is a perfect cube.