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 343000 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, ∛343000 is written as 343000(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 343000, then y3 can be 343000. Since 343000 is not a perfect cube, the cube root is approximately 70.999.
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 343000. 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 343000 is not a perfect cube, we use Halley’s method.
Let's find the cube root of 343000 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 = 343000;
x = 70
∛a ≅ 70((703 + 2 × 343000) / (2 × 703 + 343000))
∛343000 ≅ 70.999
The cube root of 343000 is approximately 70.999.
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 the ways to avoid them:
Imagine you have a cube-shaped storage container that has a total volume of 343000 cubic centimeters. Find the length of one side of the container equal to its cube root.
Side of the cube = ∛343000 ≈ 70.999 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 70.999 units.
A company manufactures 343000 cubic meters of material. Calculate the amount of material left after using 12000 cubic meters.
The amount of material left is 331000 cubic meters.
To find the remaining material, we need to subtract the used material from the total amount: 343000 - 12000 = 331000 cubic meters.
A storage tank holds 343000 cubic meters of volume. Another tank holds a volume of 8000 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 351000 cubic meters.
Let’s add the volume of both tanks: 343000 + 8000 = 351000 cubic meters.
When the cube root of 343000 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 70.999 ≈ 141.998 The cube of 141.998 ≈ 2856119.992
When we multiply the cube root of 343000 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Find ∛(46000 + 46000).
∛(46000 + 46000) = ∛92000 ≈ 44.989
As shown in the question ∛(46000 + 46000), we can simplify that by adding them.
So, 46000 + 46000 = 92000.
Then we use this step: ∛92000 ≈ 44.989 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.