Cube Root of 343 Solved Examples
Example 1: Simplify this expression: 2 × ∛343 + 10?
Solution:
We know, ∛343 = 7.
2 × ∛343 + 10 = 2(7) + 10 = 14 + 10 = 24
Example 2: The volume of a spherical ball is 343π in3. What is the radius of this ball?
Solution:
Volume of the spherical ball = 343π in3
⇒ 343π = 4/3 × π × R3
⇒ R3 = 3/4 × 343
⇒ R = ∛(3/4 × 343)
⇒ R = ∛(3/4) × ∛343
⇒ R = 0.90856 × 7 (∵ ∛(3/4) = 0.90856 and ∛343 = 7)
Thus, R is 6.35992 in3.
Example 3: 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 4: Find the real root of the equation x3 − 343 = 0.
Solution:
x3 − 343 = 0 i.e. x3 = 343
⇒ x = ∛343, x = (-7 + 7√3i)/2 and x = (-7 – 7√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 x3 − 343 = 0 is 7.
Cube Root of 343
Cube Root of 343 is 7. This is because 7 multiplied by itself three times (7 × 7 × 7) equals 343. Therefore, the cube root of 343 is the number that, when multiplied by itself three times, equals 343, and that number is 7. In this article, we will learn about Cube Root of 343, its value and methods to calculate it.
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