Cube Root Of 343 by prime factorisation method
When we multiply a number three times by itself, the result we get is said to be the cube of that number. The cube root is the inverse function of the cube of a number. In this article, we are going to learn about the cube root of 343 and the prime factorization method to find the cube root of 343.
Cube Root of 343
Meaning of cube root
When the number is multiplied three times by itself, we get the cube of that number. For example- the cube of 4 is 64( as 4 x 4 x 4 =64). The cube root is the inverse function of the cube of a number. For example, the cube root of 64 is 4(as 4, when multiplied by itself three times, gives 64).
Method of finding the cube root of 343
PRIME FACTORISATION METHOD
The prime factorization method involves the process of finding the cube root by using its prime factors. The following steps are followed in order to find the cube root of a number using the prime factorization method –
~Select a number whose cube root needs to be found, take the number 343.
~ Divide 343 with the lowest prime number. Once 343 is not divisible by that first selected prime number, select another higher prime number and carry the process until the final quotient thus obtained will be 1. Here, you can see
| 7 | 343 |
| 7 | 49 |
| 7 | 7 |
| 1 |
~Arrange the factors in the groups of threes. Here it is-7 x 7 x 7
~There is only one group of 7. So, the cube root of the number is- ∛343 = ∛73 = 7.
In this way, we can find the cube root of any number with the help of the prime factorisation method.
Illustration
Q1. When 343 is divided by 7 and 15 is added to the number, we get the cube of which number?
Sol. The prime factors of 343 = 7×7×7
When 343 is divided by 7, we get = (7×7×7)/7= 49.
When 15 is added to 49, we get = 64
The prime factors of 64 = 2×2×2×2×2×2
When we form the triplets of 2, we get = 23×23 = (2×2)3 = 43
On applying the cube root on 43, we get 4, which is the cube root of 64.
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Frequently Asked Questions
Q1.Is 7 a rational, whole number and integer?
Ans. First of all, to determine whether a number is a rational number or not. We need to see whether it can be written in the form of pq and q≠0, so we can see that 7/1 is written in the form of pq and q≠0. So, it is a rational number.
We know that the whole numbers include 0 and all natural numbers. Therefore, 7 is a whole number. An integer contains all whole numbers as well as their negatives, so 7 is also an integer.
Q2. Is the cube root of 343 a perfect cube?
Ans. We know that the cube root of 343 is 7. The prime factors of 343 are (7×7×7) = (7^3).
When we apply the cube root on 73, we get 7 as the cube root of 343. This means that 343 is the perfect cube of 7.
Q3. What is the cube root of 343?
Ans. The cube root of 343 is 7. It means that the product of 7 thrice by itself will yield the result 343.