148 LearnersLast updated on May 26th, 2025
Cube Root Of 361
A cube root of a number is a value, when it is multiplied by itself three times, gives the original number. Imagine you have a cube (box) with the known volume. The cube root helps us determine the length of one side of the box.
What Is The Cube Root Of 361?
The cube root of 361 is the number which, when multiplied three times, we get a number that is equal to 361. Let’s explore some steps and methods to calculate the cube root of 361.
The cube root of 361: ∛361 = 7.12
The exponential form of the cube root of 361: 3611/3
The radical form of the cube root of 361: ∛361
Finding The Cube Root Of 361
To find the cube root of 361, we use the following methods:
- Prime factorization
- Approximation method
- Long division
- Subtraction method
- Halley’s method is used for those numbers which are not perfect cubes.
Cube Root Of 361 By Halley’s Method
We use the below formula to find the cube root using Halley’s Method;
∛a ≅ x((x3+2a) / (2x3+a))
In the formula;
a = given number, 361
x = an approximate number close to the cube root of the number, 361: 73= 343
Let’s apply the formula and find the Cube Root:
A = 361, for the approximate method we choose, x = 7, it is the nearest cube (73= 343).
Now apply the formula;
∛a ≅ x((x3+2a) / (2x3+a))
∛361 ≅ 7((73+2 × 361) / (2 × 73+361)) = 7.12
Hence, the approximate cube of 361 ≅ 7.12
Common Mistakes and How to Avoid Them in Cube Root of 361
While learning about cube roots, children making mistakes is common, so to avoid a few mistakes that are likely to happen, below are a few mistakes and how to avoid these:
Mistake 1
Getting confused with the cube root and square root
Students sometimes multiply the same number twice instead of thrice, which makes it a square root and not a cube root. Because of this, improper results are to be found. To avoid these, students should practice square roots and cube roots regularly.
Cube Root of 361 Examples
Problem 1
Find the value of x if x³ = 361
x³ = 361
To find x, take the cube root of both sides. X = ∛361 = 7.12.
Explanation
To solve x³ = 361, find the cube root of 361, which is approximately 7.1. This gives x.
Problem 2
Find the cube root of 361 and multiply it by 5.
∛361 = 7.12
7.12 × 5 = 35.6
Explanation
The cube root of 361 is 7.12. Then, multiply that result by 5. It gives 35.6
Problem 3
Find the cube root of 361 and subtract 3.
.∛361 = 7.12
7.12 – 3= 4.12.
Explanation
The cube root of 361 is 7.12. Now subtract 3 from 7.12 it gives 4.12.
Problem 4
Find the value of (∛361) + 2.
∛361 = 7.12
(7.12+2) = 9.12.
Explanation
The cube root of 361 is about 7.12. Adding 2 to 7.12 gives 9.12 as the answer
FAQs For Cube Root Of 361
1.What is the cube root of 361?
2. Is 361 a perfect cube?
3.How is the cube root different from the square root?
4.Can the cube root of 361 be written as a fraction?
5. What is the cube root of 361 in exponential form?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Cube Root Of 361?
8.How do technology and digital tools in Oman support learning Algebra and Cube Root Of 361?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for Cube Root of 361
- Whole numbers — The whole numbers are the set of numbers that consists of natural numbers and zero. Example: 0,1,2,3………..
- Square root —A number’s square root is considered a number that when it is multiplied by itself results in the same number. Example: √4 is 2.
- Exponent: It is a number which represents how many times a base number should be multiplied.Example: 42=4 x 4 = 16
- Irrational number: The number that cannot be expressed in the form of fraction. Example: √2 is an irrational number.
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Jaskaran Singh Saluja
About the Author
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
