102 LearnersLast updated on May 26th, 2025
Cube Root of -343
A number that, when multiplied by itself three times, results in the original number is its cube root. It has various uses in real life, such as determining the dimensions of cube-shaped objects and in engineering designs. We will now find the cube root of -343 and explain the methods used.
What is the Cube Root of -343?
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, ∛-343 is written as (-343)^(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 -343, then y^3 can be -343. The cube root of -343 is -7, as (-7) × (-7) × (-7) = -343.
Finding the Cube Root of -343
Finding the cube root of a number involves identifying 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 -343. 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 such as -343, the prime factorization method is straightforward and effective.
Cube Root of -343 by Prime Factorization Method
Let's find the cube root of -343 using the prime factorization method: 1. Prime factorize -343: The prime factors of 343 are 7 × 7 × 7 = 343, and because it is negative, we have -1 as well. 2. Group the factors into triples: (-1) × (7 × 7 × 7). 3. The cube root is the single factor from each group: ∛-343 = -7. Therefore, the cube root of -343 is -7.
Common Mistakes and How to Avoid Them in the Cube Root of -343
Finding the cube root of a number without any errors can be challenging. Here are a few mistakes commonly made and ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-cube numbers.
Students often try to calculate an exact whole number for the cube root of non-cube numbers. For example, they might assume -343 has no exact cube root. To avoid this error, memorize that some numbers, like -343, are indeed perfect cubes with exact roots.
Mistake 2
Ignoring the exponent form
Many might forget that the cube root can also be written in exponent form. For example, the cube root of -343 can be expressed as (-343)^(1/3). Remember to recognize and use different forms to express cube roots.
Mistake 3
Confusing cube root with division
Some assume finding the cube root of -343 is equivalent to dividing it by 3. For example, mistakenly assuming ∛-343 = -343 ÷ 3. To avoid this, remember that the cube root of a number is the number that, when multiplied by itself three times, gives the original number.
Mistake 4
Using incorrect methods for perfect cubes
Instead of using the prime factorization method for perfect cubes, students might try unnecessary complex methods. To avoid this, recognize when a number is a perfect cube and apply the most efficient method, like prime factorization for -343.
Mistake 5
Rounding unnecessarily
Rounding the cube root too early can lead to errors. For example, rounding the cube root of -343 to a non-exact figure. To avoid this, ensure the whole calculation is done without rounding when dealing with perfect cubes.
Cube Root of -343 Examples:
Problem 1
Imagine you have a cube-shaped box with a total volume of -343 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛-343 = -7 units
Explanation
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 -7 units.
Problem 2
If a company manufactures -343 cubic meters of material, calculate the amount of material if 49 cubic meters are added to it.
The total amount of material is -294 cubic meters.
Explanation
To find the new total, add the additional material to the original amount: -343 + 49 = -294 cubic meters.
Problem 3
A container holds -343 cubic meters of liquid. Another container holds a volume of 343 cubic meters. What would be the total volume if the containers are combined?
The total volume of the combined containers is 0 cubic meters.
Explanation
Add the volumes of both containers: -343 + 343 = 0 cubic meters.
Problem 4
When the cube root of -343 is multiplied by 3, what is the resultant value?
3 × (-7) = -21
Explanation
Multiplying the cube root of -343, which is -7, by 3 results in -21.
Problem 5
Find ∛(-686 + 343).
∛(-686 + 343) = ∛-343 = -7
Explanation
Simplify the expression: -686 + 343 = -343. Then, find the cube root: ∛-343 = -7.
FAQs on -343 Cube Root
1.Can we find the Cube Root of -343?
2.Why is the Cube Root of -343 rational?
3.Is it possible to get the cube root of -343 as an exact number?
4.Can we find the cube root of any number using prime factorization?
5.Is there any formula to find the cube root of a number?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Cube Root of -343?
8.How do technology and digital tools in Canada support learning Algebra and Cube Root of -343?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for Cube Root of -343
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 if it is the product of multiplying a number three times by itself. For example, (-7) × (-7) × (-7) = -343, so -343 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a^(1/3), ⅓ is the exponent denoting the cube root. Radical sign: The symbol used to represent a root, expressed as ∛. Rational number: A number that can be expressed as a fraction. The cube root of -343 is rational because it is -7.
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Jaskaran Singh Saluja
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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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