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 51200 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, ∛51200 is written as ( 51200{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 51200, then ( y3 ) can be 51200. Since the cube root of 51200 is not an exact whole number, we can approximate it as 37.276.
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 51200. The common methods we follow to find the cube root are given below:
To find the cube root of a non-perfect number, we often follow Halley’s method. Since 51200 is not a perfect cube, we use Halley’s method.
Let's find the cube root of 51200 using Halley’s method.
The formula is ∛a ≅ x((x³ + 2a) / (2x³ + a))
where: a = the number for which the cube root is being calculated
x = the nearest perfect cube
Substituting, a = 51200;
x = 37
∛a ≅ 37((37³ + 2 × 51200) / (2 × 37³ + 51200))
∛51200 ≅ 37.275
The cube root of 51200 is approximately 37.276.
Finding the perfect cube 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 storage container that has a total volume of 51200 cubic centimeters. Find the length of one side of the container equal to its cube root.
Side of the cube = ∛51200 ≈ 37.28 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 approximately 37.28 units.
A company manufactures 51200 cubic meters of material. Calculate the amount of material left after using 15000 cubic meters.
The amount of material left is 36200 cubic meters.
To find the remaining material, we need to subtract the used material from the total amount:
51200 - 15000 = 36200 cubic meters.
A tank holds 51200 liters of water. Another tank holds a volume of 8000 liters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 59200 liters.
To find the total volume, add the volume of both tanks:
51200 + 8000 = 59200 liters.
When the cube root of 51200 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 37.28 ≈ 74.56 The cube of 74.56 ≈ 414394.88
When we multiply the cube root of 51200 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Find ∛(46000 + 5200).
∛(46000 + 5200) = ∛51200 ≈ 37.28
As shown in the question ∛(46000 + 5200), we can simplify that by adding them.
So, 46000 + 5200 = 51200.
Then we use this step: ∛51200 ≈ 37.28 to get the answer.
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.