Calculate $\sqrt[3]{343}$
Answer (2)
We need to find a number x such that x 3 = 343 .
Test integer values: 1 3 = 1 , 2 3 = 8 , 3 3 = 27 , 4 3 = 64 , 5 3 = 125 , 6 3 = 216 , 7 3 = 343 .
Since 7 3 = 343 , the cube root of 343 is 7.
The cube root of 343 is 7 .
Explanation
Understanding the Cube Root We are asked to calculate the cube root of 343, which means we need to find a number that, when multiplied by itself three times, equals 343. In mathematical terms, we want to find x such that x 3 = 343 .
Testing Integer Values Let's start by testing small integers to see if their cube equals 343. We can try a few numbers:
1 3 = 1 × 1 × 1 = 1 2 3 = 2 × 2 × 2 = 8 3 3 = 3 × 3 × 3 = 27 4 3 = 4 × 4 × 4 = 64 5 3 = 5 × 5 × 5 = 125 6 3 = 6 × 6 × 6 = 216 7 3 = 7 × 7 × 7 = 343
Identifying the Cube Root We found that 7 3 = 343 . Therefore, the cube root of 343 is 7.
Final Answer Thus, the cube root of 343 is 7 .
Examples
Imagine you're designing a cubic box to hold exactly 343 unit cubes. To find the length of one side of the box, you need to calculate the cube root of 343. In this case, the side length would be 7 units, since 7 × 7 × 7 = 343 . This concept is useful in various fields like packaging design, architecture, and engineering, where understanding volumes and dimensions is crucial.
The cube root of 343 is 7, as 7 multiplied by itself three times ( 7 3 ) equals 343. Therefore, 3 343 = 7 .
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