How do you find the cubed root of $343$ ?

Hint:
Normally, we utilize a prime factorization strategy to locate the prime factors of the given number. Consequently, on the off chance that we assess prime factors of $343$ , at that point, we need to combine them in a pair of three which will give the factors. Subsequently, whenever we have discovered the cube root of factors of a number, we can apply the cube root, which gets dropped with the cubes.

Complete Step by Step Solution:
First of all, we have to evaluate the prime factors of $343$
So, it will be equal to
$ \Rightarrow 343 = 7 \times 7 \times 7$
We can see $343$ is a perfect square. Hence, now we will group the factors in such a way that it will be the pair of three and we can write it in the form of cubes
$ \Rightarrow 343 = {7^3}$
Now on multiplying with the cube root both the side of the above equation, we get
$\sqrt[3]{{343}} = \sqrt[3]{{{7^3}}}$
So, here in the above equation, the cube root will be canceled by the cube of $7$ .
Therefore, $\sqrt[3]{{343}} = 7$

Hence, the cubed root of $343$ is $7$.

Note:
Here, we had seen the steps for calculating the cube root. It is recommended that we memorize the cubed root till the $10$ . As we can easily find the perfect cubes up to three-digit of the numbers. And for four-digit numbers, we can use the estimation method. In this method, we have to make a group of three-digit and it should be started from the right and from the first group we will take the number which is at one place. That number will be the unit digit of the cube. Similarly, for the second group, we will estimate the cube root by taking one and third digits into consideration, and then we will get the cube root of that whole number.