cube root of 196
Understand the Problem
The question is asking for the cube root of the number 196. The cube root of a number x is the value that, when multiplied by itself three times, gives the original number x.
Answer
The cube root of 196 is approximately $5.82$.
Answer for screen readers
The cube root of 196 is approximately ( 5.82 ).
Steps to Solve
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Identify the cube root notation The cube root of a number ( x ) is represented as ( \sqrt[3]{x} ). In this case, we need to calculate ( \sqrt[3]{196} ).
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Approximate the cube root To find ( \sqrt[3]{196} ), we can calculate the cube roots of perfect cubes around 196. The cube of 5 is ( 125 ) and the cube of 6 is ( 216 ). Since ( 196 ) lies between these two cubes, we can conclude that: $$ 5 < \sqrt[3]{196} < 6 $$
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Use a calculator or estimation method For a more precise answer, we can use a calculator to compute the cube root. If you calculate ( \sqrt[3]{196} ), you will find that it is approximately ( 5.82 ).
The cube root of 196 is approximately ( 5.82 ).
More Information
The cube root is a mathematical operation that reflects the inverse of cubing a number. It means finding a number that, when multiplied by itself three times, results in the original number. Cube roots are often used in geometry and physics.
Tips
A common mistake is miscalculating the cube root or confusing it with the square root. It's important to remember that the cube root means finding a number that when cubed equals the given number, not squared.
