Evaluate $\sqrt[4]{16}$
Answer (2)
Evaluate the fourth root of 16: 4 16 = 2 .
Identify the index of the radical expression 3 2 7 : The index is 3.
The answer to the first question is 2.
The answer to the second question is 3. 2 ; 3
Explanation
Evaluating the Fourth Root of 16 Let's tackle these questions one by one! First, we need to evaluate 4 16 . This means we're looking for a number that, when raised to the fourth power, equals 16.
Calculating the Root We can express 4 16 as 1 6 4 1 . Since 2 4 = 2 × 2 × 2 × 2 = 16 , we know that 4 16 = 2 .
Identifying the Index Next, we need to identify the index of the radical expression 3 2 7 . The index is the small number written above and to the left of the radical symbol. In this case, the index is 3.
Final Answers Therefore, the answer to the first question is 2, and the answer to the second question is 3.
Examples
Understanding roots and indices is crucial in many fields, such as engineering and computer science. For example, when designing structures, engineers need to calculate the square root of areas or volumes to ensure stability. In computer graphics, indices are used to manipulate and render images efficiently. Knowing how to work with roots and indices allows professionals to solve complex problems and create innovative solutions.
The fourth root of 16 is 2, since 4 16 = 4 2 4 = 2 . This means that if you raise 2 to the fourth power, you will get 16. Hence, the evaluation of 4 16 results in 2.
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