Last updated on May 26th, 2025
A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of -729 and explain the methods used.
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓. In exponential form, ∛(-729) is written as (-729)^(1/3). The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of -729, then y^3 can be -729. The cube root of -729 is -9 because (-9) × (-9) × (-9) = -729.
Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of -729. The common methods we follow to find the cube root are given below: Prime factorization method Approximation method Subtraction method Halley’s method To find the cube root of a perfect cube like -729, the prime factorization method is very effective.
Let's find the cube root of -729 using the prime factorization method. First, factor -729 into its prime factors: -729 = -1 × 3 × 3 × 3 × 3 × 3 × 3. We group the factors into sets of three: (-1) × (3 × 3 × 3) × (3 × 3 × 3). Each set of three identical factors gives one factor of the cube root. Thus, ∛(-729) = -3. The cube root of -729 is -9.
Finding the cube root of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes students commonly make and the ways to avoid them:
Imagine you have a cube-shaped object with a total volume of -729 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛(-729) = -9 units
To find the side of the cube, we need to find the cube root of the given volume. Therefore, the side length of the cube is -9 units, indicating the direction or nature of the measurement.
A company has a cube of material with a volume of -729 cubic meters. Calculate the amount of material left after using -243 cubic meters.
The amount of material left is -486 cubic meters.
To find the remaining material, we need to subtract the used material from the total amount: -729 - (-243) = -486 cubic meters.
A container has a volume of -729 cubic meters, and another has a volume of -81 cubic meters. What would be the total volume if the containers are combined?
The total volume of the combined containers is -810 cubic meters.
Explanation: Add the volume of both containers: -729 + (-81) = -810 cubic meters.
When the cube root of -729 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × (-9) = -18 The cube of -18 = -5832
When we multiply the cube root of -729 by 2, it results in a significant increase in magnitude because the cube increases exponentially, resulting in -5832.
Find ∛(-64 - 64).
∛(-64 - 64) = ∛(-128) ≈ -5.04
As shown in the question ∛(-64 - 64), we can simplify that by adding them. So, -64 - 64 = -128. Then we use this step: ∛(-128) ≈ -5.04 to get the answer.
Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number. Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. For example, (-9) × (-9) × (-9) = -729, therefore, -729 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (-729)^(1/3), ⅓ is the exponent which denotes the cube root of -729. Radical sign: The symbol that is used to represent a root which is expressed as (∛). Negative cube root: A negative number that, when multiplied by itself three times, results in a negative perfect cube. For example, ∛(-729) = -9.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.