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Last updated on February 13th, 2025

Cube Root Of 361

Q: Is 361 a perfect cube?

No, 361 is not a perfect cube because there is no integer whose cube equals 361

Q: How is the cube root different from the square root?

The cube root is the value that, when multiplied by itself three times, is the same as the number. The square root gets a value which is multiplied with itself twice.

Q: Can the cube root of 361 be written as a fraction?

The cube root of 361 cannot be expressed as a simple fraction, since it's an irrational number.

Q: What is the cube root of 361 in exponential form?

The cube root of 361 in the form of an exponential is the expression 3611/3.

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

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: 361^1/3

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

Cube Root of 361 Examples

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

Find the value of x if x³ = 361

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Explanation

Problem 2

Find the cube root of 361 and multiply it by 5.

Explanation

Problem 3

Find the cube root of 361 and subtract 3.

Explanation

Problem 4

Find the value of (∛361) + 2.

Explanation

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?

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.