Cube Root of 343
The cube root of 343, denoted as ^{3}√343, is a value that gives the original value when we multiply it three times by itself. This is the basic definition of the cube root. If a number is a perfect cube, we can easily find the cube root of a number. In this article, we will find the value of cube root of 343, using the prime factorization method and examples with complete explanation.
What is the Value of Cube Root of 343?
The cube root of a number 343, is a number which when multiplied by itself three times results in the original number 343. The cube root of 343 is symbolically represented as ^{3}√343.
^{3}√343 = ^{3}√(Number × Number × Number)
^{3}√343 = ^{3}√(7×7×7) = 7
Cube root of 343, ^{3}√343 = 7 |
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 = 7^{3}
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}√(7^{3})
So, here the cube root is cancelled by the cube of 7.
Hence, ^{3}√343 = 7
Hence, the value of cube root of 343 is 7.
Also, check:
Cube Root of Numbers
Now, let us have a look at the cube root of different numbers in brief:
Number (n) | Cube Root of a Number (^{3}√n) |
1 |
1 |
8 |
2 |
27 |
3 |
64 |
4 |
125 |
5 |
216 |
6 |
343 |
7 |
512 |
8 |
729 |
9 |
1000 |
10 |
Examples
Example 1:
Simplify the expression: 2× ^{3}√343+ 10
Solution:
Given expression:2× ^{3}√343 + 10
We know that ^{3}√343 is 7.
Now, substitute the value in the given expression, we get
2×^{3}√343 + 10 = 2(7) + 10
2×^{3}√343 + 10 = 14+10 = 24.
Hence, 2×^{3}√343 + 10 = 24.
Example 2:
Find the value of k, if k ×^{3}√343= 35.
Solution:
Given equation: k ×^{3}√343= 35.
The value of cube root of 343 is 7.
Now, substitute value in the expression, we get
k(7) = 35
k = 35/7
k = 5
Therefore, the value of k is 5.
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Frequently Asked Questions on Cube Root of 343
What is the value of cube root of 343?
The value of cube root of 343 is 7.
Is 343 a perfect cube number?
Yes, 343 is a perfect cube number, as it can be expressed as the product of three equal integers.
Is the cube root of 343 a rational number?
Yes, the cube root of 343 is a rational number, as it can be written in the form of p/q.
What is the value of cube of cube root of 343?
The value of cube of cube root of 343 is 343.
(i.e) (^{3}√343)^{3} = 343.
What is the value of 10 plus cube root of 343?
We know that the cube root of 343 is 7.
Hence, 10+^{3}√343 = 10+7 = 17.