Which of the following simplifies to 4?
Responses
12−−√
square root of 12
16−−√
square root of 16
8√
square root of 8
4√
square root of 16
To determine which of the given expressions simplifies to 4, we need to evaluate each expression.
1. 12−−√:
The square root of 12 is approximately 3.464. Therefore, 12−−√ is not equal to 4.
2. 16−−√:
The square root of 16 is 4. Therefore, 16−−√ simplifies to 4.
3. 8√:
The square root of 8 is approximately 2.828. Therefore, 8√ is not equal to 4.
4. 4√:
The square root of 4 is 2. Therefore, 4√ simplifies to 2.
From the given options, only 16−−√ simplifies to 4.
To determine which of the options simplifies to 4, we need to calculate the square root of each option and check if it equals 4.
Let's calculate the square roots of the given options:
1. Square root of 12: √12 ≈ 3.464
2. Square root of 16: √16 = 4
3. Square root of 8: √8 ≈ 2.828
4. Square root of 4: √4 = 2
From the calculations, we can see that the only option that simplifies to 4 is the square root of 16.
Therefore, the correct option is "16−−√", which is the square root of 16.