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 610 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, ∛610 is written as 610(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 610, then y3 can be 610. Since the cube root of 610 is not an exact value, we can write it as approximately 8.534.
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 610. The common methods we follow to find the cube root are given below:
To find the cube root of a non-perfect cube number, we often follow Halley’s method. Since 610 is not a perfect cube, we use Halley’s method.
Let's find the cube root of 610 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 = 610; x = 8
∛a ≅ 8((83 + 2 × 610) / (2 × 83 + 610))
∛610 ≅ 8((512 + 1220) / (1024 + 610))
∛610 ≅ 8.534
The cube root of 610 is approximately 8.534.
Finding the perfect cube 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 ways to avoid them:
Imagine you have a cube-shaped toy that has a total volume of 610 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛610 = 8.534 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 8.534 units.
A company manufactures 610 cubic meters of material. Calculate the amount of material left after using 150 cubic meters.
The amount of material left is 460 cubic meters.
To find the remaining material,
we need to subtract the used material from the total amount:
610 - 150 = 460 cubic meters.
A bottle holds 610 cubic meters of volume. Another bottle holds a volume of 200 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 810 cubic meters.
Let’s add the volume of both bottles:
610 + 200 = 810 cubic meters.
When the cube root of 610 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 8.534 = 17.068
The cube of 17.068 ≈ 4972.648
When we multiply the cube root of 610 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Find ∛(305 + 305).
∛(305 + 305) = ∛610 ≈ 8.534
As shown in the question ∛(305 + 305), we can simplify that by adding them.
So, 305 + 305 = 610.
Then we use this step: ∛610 ≈ 8.534 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.