Cube Root of 343

Dhristi JEE 2022-24

Introduction

Cube root of 343, represented as 3√343, is a value that returns the original value when multiplied three times by itself. This is the most fundamental definition of a cube root. If an integer is a perfect cube, we can calculate its cube root. We shall get the value of the cube root of 343 in this article by utilizing the prime factorization technique and examples with detailed explanations.


What is the Cube Root?

When a number (x) is multiplied three times, the resulting number is called its cube. As a result, the cube of (x) becomes x3 or x-cubed.


For Example: If we multiply 9 three times, we get 729.


9 x 9 x 9 = 729.. Thus, 9 will be referred to as the cube root of 729.


Symbol of a Cube Root 

The symbol that we use to represent a cube root is the same as that of a square root with the only difference that in a square root, we use the number 2 and in cube root, we use the number 3. The root symbol can also be called a radical symbol. Here is how we represent a cube root:

∛x


What is the Cube Root of 343?

The cube root of 343 is the integer that, when multiplied three times by itself, produces the result 343. Because 343 can be written as 7 7 7. As a result, the cube root of 343 is ∛(7 × 7 × 7) = 7.


Ways to find Cube root

Typically, we apply the prime factorization method to discover the prime factors of a given number. Therefore, if we examine 343 prime factors, we must organize them into groups of three, which provides the cube of factors. Thus, once we have determined the cube of a number's factors, we can apply the cube root, which cancels out the cubes.


Step-by-Step Procedure to find a Prime Factor of 343

  • Step 1:

Determine the prime factors of 343.


343 equals 7 x 7 x 7


  • Step 2:

It is self-evident that 343 is a perfect cube. As a result, arrange the 343 components into three pairs and write them as cubes.


343 equals 7x7x7


343 = 73


  • Step 3:

We will apply the cube root to both sides of the preceding statement to eliminate the word in cubes.


3√343 = 3√(73)


  • Thus, the cube root is canceled out in this case by the cube of 7.


As a result, 3√343 = 7


  • As a result, the value of 343's cube root is 7.


Examples of Cube Root of 343

Example 1: What is the cube root of 15625?

Solution:

5x5x5x5x5x5 is the cube root of 15625.


= (5x5)x(5x5)x(5x5)


=25x25x25


As a result, 25 equals the cube root of 1562


Example 2: Simplify this expression: 2× 3√343+ 10?

Solution:

We know, 3√343 = 7.


Now, substitute this into the expression.


2×3√343 + 10 = 2(7) + 10


2×3√343 + 10 = 14+10 = 24.


=2×3√343 + 10 = 24.


Example 3: What can the smallest integer be divided by 73002 to form a perfect cube?

Solution:

73002 has a prime factorization of 23 x 23 x 23 x 2 x 3.


There is already a set of three 23s here, but only 2 and 3 remain. Thus, by dividing the number by 6, we may obtain a perfect cube.

FAQs on Cube Root of 343

1. Is 343 a perfect cube?

Yes, We can get 343 from the product of three equal integers, and that's why 343 is a perfect cube.

2. Is the cube of 343 a rational number?

Yes, The cube of 343 is a rational number because it can be represented as p/q.

3. What is the value of 15 plus the cube root of 343?

The cube root of 343 = 7.


Hence, 7+15 = 22.

4. What is the value of ∛0.343? When do we know the cube of 343?

Consider the following representation of ∛0.343 in p/q form: ∛(343/1000) = 7/10 = 0.7. As a result, the value of ∛0.343 equals 0.7.

5. How to simplify the cube root of 343/729?

We know that the cube root of 343 is 7, and the cube root of 729 is 9. Therefore, ∛(343/512) = (∛343)/(∛729) = 7/9 = 0.778.

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