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.

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., 7³or 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.

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.

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.