Cube Root of 343
The value of the cube root of 343 is 7. It is the real solution of the equation x^{3} = 343. The cube root of 343 is expressed as ∛343 in radical form and as (343)^{⅓} or (343)^{0.33} in the exponent form. As the cube root of 343 is a whole number, 343 is a perfect cube.
 Cube root of 343: 7
 Cube root of 343 in exponential form: (343)^{⅓}
 Cube root of 343 in radical form: ∛343
1.  What is the Cube Root of 343? 
2.  How to Calculate the Cube Root of 343? 
3.  Is the Cube Root of 343 Irrational? 
4.  FAQs on Cube Root of 343 
What is the Cube Root of 343?
The cube root of 343 is the number which when multiplied by itself three times gives the product as 343. Since 343 can be expressed as 7 × 7 × 7. Therefore, the cube root of 343 = ∛(7 × 7 × 7) = 7.
How to Calculate the Value of the Cube Root of 343?
Cube Root of 343 by Prime Factorization
 Prime factorization of 343 is 7 × 7 × 7
 Simplifying the above expression: 7^{3}
Therefore, the cube root of 343 by prime factorization is (7 × 7 × 7)^{1/3} = 7.
Is the Cube Root of 343 Irrational?
No, because ∛343 = ∛(7 × 7 × 7) can be expressed in the form of p/q i.e. 7/1. Therefore, the value of the cube root of 343 is an integer (rational).
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Cube Root of 343 Solved Examples

Example 1: The volume of a spherical ball is 343π in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = 343π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 3/4 × 343
⇒ R = ∛(3/4 × 343) = ∛(3/4) × ∛343 = 0.90856 × 7 (∵ ∛(3/4) = 0.90856 and ∛343 = 7)
⇒ R = 6.35992 in^{3} 
Example 2: What is the value of ∛343 + ∛(343)?
Solution:
The cube root of 343 is equal to the negative of the cube root of 343.
i.e. ∛343 = ∛343
Therefore, ∛343 + ∛(343) = ∛343  ∛343 = 0 
Example 3: Find the real root of the equation x^{3} − 343 = 0.
Solution:
x^{3} − 343 = 0 i.e. x^{3} = 343
Solving for x gives us,
x = ∛343, x = ∛343 × (1 + √3i))/2 and x = ∛343 × (1  √3i))/2
where i is called the imaginary unit and is equal to √1.
Ignoring imaginary roots,
x = ∛343
Therefore, the real root of the equation x^{3} − 343 = 0 is for x = ∛343 = 7.
FAQs on Cube Root of 343
What is the Value of the Cube Root of 343?
We can express 343 as 7 × 7 × 7 i.e. ∛343 = ∛(7 × 7 × 7) = 7. Therefore, the value of the cube root of 343 is 7.
How to Simplify the Cube Root of 343/512?
We know that the cube root of 343 is 7 and the cube root of 512 is 8. Therefore, ∛(343/512) = (∛343)/(∛512) = 7/8 = 0.875.
Why is the value of the Cube Root of 343 Rational?
The value of the cube root of 343 can be expressed in the form of p/q i.e. = 7/1, where q ≠ 0. Therefore, the ∛343 is rational.
What is the Value of 9 Plus 8 Cube Root 343?
The value of ∛343 is 7. So, 9 + 8 × ∛343 = 9 + 8 × 7 = 65. Hence, the value of 9 plus 8 cube root 343 is 65.
If the Cube Root of 343 is 7, Find the Value of ∛0.343.
Let us represent ∛0.343 in p/q form i.e. ∛(343/1000) = 7/10 = 0.7. Hence, the value of ∛0.343 = 0.7.
Is 343 a Perfect Cube?
The number 343 on prime factorization gives 7 × 7 × 7. On combining the prime factors in groups of 3 gives 7. So, the cube root of 343 = ∛(7 × 7 × 7) = 7 (perfect cube).
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