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Last updated on December 2nd, 2024

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Cube root of 343

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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.

Cube root of 343 for Australian Students
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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. 
 

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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 
 

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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. 

 

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

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Cube Root of 343 Examples

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Problem 1

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

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Explanation

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Problem 2

What is the value of (7)¹/³

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Explanation

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Problem 3

Find ∛343/ ∛8

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Explanation

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Problem 4

What is ∛(7²) ?

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Explanation

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FAQs on 343 Cube Root

1.What is 343 divisible by?

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2.What is square root of 343?

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3.What is the LCM of 343

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4.Is 3√343 irrational?

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5.Is 343 a multiple of 9

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6.What is the value of 5√ 5

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7.How does learning Algebra help students in Australia make better decisions in daily life?

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8.How can cultural or local activities in Australia support learning Algebra topics such as Cube root of 343?

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9.How do technology and digital tools in Australia support learning Algebra and Cube root of 343?

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10.Does learning Algebra support future career opportunities for students in Australia?

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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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About BrightChamps in Australia

At BrightChamps, we know algebra is more than just digits—it’s the gateway to endless opportunities! Our mission is to help children across Australia develop essential math skills, focusing today on the Cube root of 343 with a special emphasis on cube roots—in a way that’s engaging, enjoyable, and easy to understand. Whether your child is calculating the speed of a roller coaster at Luna Park Sydney, keeping score at a local cricket match, or managing their allowance to buy the latest gadgets, mastering algebra gives them the confidence they need for everyday situations. Our interactive lessons keep learning simple and fun. Since kids in Australia learn in various ways, we tailor our teaching to fit each learner’s style. From the vibrant streets of Sydney to the beautiful beaches of the Gold Coast, BrightChamps brings math to life, making it exciting across Australia. Let’s make cube roots a fun part of every child’s math journey!
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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.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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