Which is the BEST term to describe the number 125 in the equation $\sqrt[3]{125}=5$?
A. rational exponent
B. perfect cube
C. perfect square
D. index
Answer (2)
Perfect cube is a number that can be obtained by cubing an integer.
5 3 = 125 , so 125 is a perfect cube.
Perfect square is a number that can be obtained by squaring an integer, and 125 is not a perfect square.
The best term to describe the number 125 is p er f ec t c u b e .
Explanation
Analyzing the Problem Let's analyze the given equation 3 125 = 5 and the options provided to determine the best term to describe the number 125.
Checking Perfect Cube A perfect cube is a number that can be obtained by cubing an integer. In other words, a perfect cube is a number of the form n 3 , where n is an integer. Since 5 3 = 5 × 5 × 5 = 125 , the number 125 is a perfect cube.
Checking Perfect Square A perfect square is a number that can be obtained by squaring an integer. In other words, a perfect square is a number of the form n 2 , where n is an integer. Since 1 1 2 = 121 and 1 2 2 = 144 , 125 is not a perfect square.
Checking Rational Exponent A rational exponent is an exponent that can be expressed as a fraction q p , where p and q are integers. In the given equation, the exponent is 3 1 , which is a rational exponent. However, the question asks for the best term to describe the number 125, not the exponent.
Checking Index The index of a radical is the small number written above and to the left of the radical symbol. In the equation 3 125 = 5 , the index is 3. However, the question asks for the best term to describe the number 125, not the index.
Conclusion Based on the analysis, the best term to describe the number 125 in the equation 3 125 = 5 is perfect cube .
Examples
Understanding perfect cubes is useful in various real-life scenarios. For example, when designing cubic storage containers, knowing the volume that a perfect cube can hold helps in optimizing space. Similarly, in architecture, perfect cubes can be used as a fundamental building block to create symmetrical and aesthetically pleasing structures. Recognizing perfect cubes also aids in simplifying mathematical problems related to volumes and dimensions.
The best term to describe the number 125 in the equation 3 125 = 5 is perfect cube, as it can be expressed as 5 3 . Other terms such as perfect square or rational exponent do not correctly describe 125. Therefore, the correct answer is B. perfect cube .
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