Cube Root of 343

The cube root of 343, denoted as 3√343, is a value which gives the original value when we multiply it three times by itself. This is the basic definition of the cube root. Suppose, ‘n’ is the value of 3√343, then n × n × n = n3 = 343. In this article, we will find the value of n, using the prime factorisation method.

Cube root of 343, 3√343 = 7

Also, check:

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

Finding the cube root of perfect cubes up to three-digit numbers is easy if we memorise the below-given table.

Number (n)

Cubes (n3)

1

1

2

8

3

27

4

64

5

125

6

216

7

343

8

512

9

729

10

1000

But to find the cube root of four-digit numbers, we need to use the estimation method.

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