Cube Root of 343

The cube root of 343, denoted as ³√343, is a value that gives the original value when we multiply it three times by itself. This is the basic definition of the cube root.  If a number is a perfect cube, we can easily find the cube root of a number. In this article, we will find the value of cube root of 343, using the prime factorization method and examples with complete explanation.

What is the Value of Cube Root of 343?

The cube root of a number 343, is a number which when multiplied by itself three times results in the original number 343. The cube root of 343 is symbolically represented as ³√343.

³√343 = ³√(Number × Number × Number)

³√343 = ³√(7×7×7) = 7

How to Find Cube Root of 343?

Usually, we use prime factorisation method to find the prime factors of the given number. Therefore, if we evaluate prime factors of 343, then we need to pair them in a group of three which will give the cube of factors. Hence, once we have found the cube of factors of a number, we can apply the cube root, which gets cancelled with the cubes.

Let us understand it in a step-by-step procedure.

Step 1: Find the prime factors of 343

343 = 7 × 7 × 7

Step 2: Clearly, 343 is a perfect cube. Therefore, group the factors of 343 in a pair of three and write in the form of cubes.

343 = 7 × 7 × 7

343 = 7³

Step 3: Now, we will apply cube root to both the sides of the above expression to take out the term in cubes.

³√343 = ³√(7³)

So, here the cube root is cancelled by the cube of 7.

Hence, ³√343 = 7

Hence, the value of cube root of 343 is 7.

Also, check:

• Cube Root Of Unity
• Square Root And Cube Root
• How to find cube root
• Cube root table

Cube Root of Numbers

Now, let us have a look at the cube root of different numbers in brief:

Video Lesson on Finding Cube Roots

Solved Examples

Example 1: 

Simplify the expression: 2× ³√343+ 10

Solution: 

Given expression:2× ³√343 + 10

We know that ³√343 is 7.

Now, substitute the value in the given expression, we get

2׳√343 + 10 = 2(7) + 10

2׳√343 + 10 = 14+10 = 24.

Hence, 2׳√343 + 10 = 24.

Example 2: 

Find the value of k, if k ×³√343= 35.

Solution:

Given equation: k ×³√343= 35.

The value of cube root of 343 is 7.

Now, substitute value in the expression, we get

k(7) = 35

k = 35/7

k = 5

Therefore, the value of k is 5.

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