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 778688 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, ∛778688 is written as 778688(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 778688, then y3 can be 778688. Since the cube root of 778688 is an exact value, it is 92.
Finding the cube root of a number is to identify the number that must be multiplied three times to result in the target number. Now, we will go through the different ways to find the cube root of 778688. The common methods we follow to find the cube root are given below:
To find the cube root of a perfect cube number, we often use the prime factorization method. Since 778688 is a perfect cube, we can use this method.
Let's find the cube root of 778688 using the prime factorization method.
Firstly, find the prime factors of 778688.
778688 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 23
We can group the factors into triples: (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (23)
= 923
Therefore, the cube root of 778688 is 92.
Finding the cube root of a number without any errors can be a difficult task for the students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:
Imagine you have a cube-shaped toy that has a total volume of 778688 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛778688 = 92 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 exactly 92 units.
A company manufactures 778688 cubic meters of material. Calculate the amount of material left after using 100000 cubic meters.
The amount of material left is 678688 cubic meters.
To find the remaining material, we need to subtract the used material from the total amount: 778688 - 100000 = 678688 cubic meters.
A bottle holds 778688 cubic meters of volume. Another bottle holds a volume of 5000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 783688 cubic meters.
Explanation: Let’s add the volume of both bottles: 778688 + 5000 = 783688 cubic meters.
When the cube root of 778688 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 92 = 184 The cube of 184 = 6229504
When we multiply the cube root of 778688 by 2, it results in a new cube root, and its cube results in a substantially larger volume because the cube increases exponentially.
Find ∛(500000 + 278688).
∛(500000 + 278688) = ∛778688 = 92
As shown in the question ∛(500000 + 278688), we can simplify that by adding them. So, 500000 + 278688 = 778688. Then we use this step: ∛778688 = 92 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. A perfect cube always results in a whole number. For example, 92 × 92 × 92 = 778688, therefore, 778688 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 778688^(1/3), ⅓ is the exponent which denotes the cube root of 778688. Radical sign: The symbol that is used to represent a root is expressed as (∛). Rational number: A number that can be expressed as the quotient or fraction of two integers. The cube root of 778688 is rational because it is an exact whole number, 92.
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.
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