[Maths Class Notes] on Cube Root of 343 Pdf for Exam

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

Determine the prime factors of 343.

343 equals 7 x 7 x 7

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

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

3√343 = 3√(73)

As a result, 3√343 = 7

Examples of Cube Root of 343

Example 1: What is the cube root of 15625?

Solution:

5x5x5x5x5x5 is the cube root of 15625.

= (5×5)x(5×5)x(5×5)

=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.