Cube root of 343
2026-02-28 09:05 Diff
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Last updated on August 5, 2025

Cube root is defined as a value which when cubed gives the original number or it can be said as the value of “y” where Itself multiplied thrice (yxyxy) equals 343. Cube roots find their uses in a wide range in our everyday activities including engineering, measuring densities and volumes of different shapes or designing open spaces.

What is the cube root of 343?

We know that 343 is a perfect cube so the cube root of 343 is equal to 7. The cube root of 343 is written as ∛343, where the sign “∛” denotes the radical. 
 

Finding the Cube Root of 343

We can find the cube root of 343, mainly through two methods: 


i) Prime Factorization method.


ii) Subtraction method 
 

Cube Root of 343 By Prime Factorization

To find a cube root of 343 the Prime Factorization method is one of the most widely and easiest methods to find the cube root of 343 that involves determining the factor of 343.


Step 1 — Find the prime factors of 343. 


So, the prime factors of 343 are 7×7×7


Step 2 — The next thing you need to do is group the factors of 343 together in a group of 3(i.e., power of 3).


Step 3 —  Here, we get the factor 7 in the power of 3, i.e., 73 or 7×7×7 


The cube root of 343 can be written as ∛343 = ∛7×7×7 = 7 


So through the above calculations, we can say that the cube root of 343 is 7.

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Cube root of 343 by Subtraction method

This method involves subtracting successive odd numbers repeatedly. The list of odd numbers that should be subtracted successively are → 1,7,19,37,61,91,127,169,217,331,397 … This iteration will continue till we get a zero. 


Step 1 — Subtract the 1st odd number : 343–1 = 342 


Step 2 — Subtract the next odd number: 342–7 = 335


Step 3 — Subtract the next odd number: 335–19 = 316


Step 4 — Subtract the next odd number: 316–37 = 279


Step 5 — Subtract the next odd number: 279–61 = 218


Step 6 — Subtract the next odd number: 218– 91 = 127


Step 7 — Subtract the next odd number: 127–127 = 00 


Here, the subtraction took place seven times to reach zero.


So from the above steps and calculations, the cube root of 343 is 7. 

Common Mistakes and How to Avoid Them in cube root of 343

When we calculate the cube root of 343, there are common errors that we all make. Now, let's talk about some of the mistakes and their solutions.
 

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Problem 1

How can you express 343 as a product of its prime factors?

Okay, lets begin

 343=7×7×7
 

Explanation

 Break down 343 into the prime factors
 

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Problem 2

What is the value of (7)¹/³

Okay, lets begin

1.913 approx
 

Explanation

The cube root of 7 is between 1 and 2 because 13 = 1 and 23 = 8. So by trial and error, you can get an approximate value that is closer to the actual value. 
 

Well explained 👍

Problem 3

Find ∛343/ ∛8

Okay, lets begin

 ∛343/ ∛8

= 7 / 2

=3.5


Answer: 3.5
 

Explanation

We know that the cubic root of 8 is 2, hence dividing  ∛343 by ∛8.
 

Well explained 👍

Problem 4

What is ∛(7²) ?

Okay, lets begin

 ∛(72)

= ∛49

= 3.659… 


Answer: 3.659… 
 

Explanation

 We first found the square value of 7, which is 49, and then found out the cube root of 49.
 

Well explained 👍

FAQs on 343 Cube Root

1.What is 343 divisible by?

The number 343 is divisible by 1,7 and 49.  
 

2.What is square root of 343?

 The square root of 343 is 18.52.
 

3.What is the LCM of 343

4.Is 3√343 irrational?

 Irrational — 3√343 (3×√343 = 3×7 = 21, which is rational)
 

5.Is 343 a multiple of 9

343 is not divisible by 9.
 

6.What is the value of 5√ 5

Important Glossaries for Cubic Root of 343

  • Mathematical Operations : Addition, Subtraction, Multiplication, Division and Exponentiation
  • Factoring:The process of breaking down a mathematical equation into its simplest form.
  • Power Of One:This is a number that when looked at can be an integer of another since number.
  • Squareroot: The square root of the number is a value (denoted by r), which, when multiplied by itself yields to the initial term as √93 = y would be that y×y = x.
  • Polynomial:A polynomial is an algebraic expression consisting of variables such as x and constants joined using addition, subtraction, multiplication or division where the variables are raised to whole-number exponents.

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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.