Evaluate 216−−−√3 .(1 point) Responses 8 8 108 108 72 72 6
The square root of 216 is 6. Therefore, the expression 216−−−√3 is equal to 6.
To evaluate √216, we can simplify it by finding the factors of 216 and identifying any perfect square factors.
The factors of 216 are:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
Among these factors, we can see that 9 is a perfect square (9 x 24 = 216).
Therefore, √216 simplifies to 9.
Hence, the correct response is 9.
To evaluate 216√3, we first need to simplify the expression. Taking the cube root of 216 gives us:
∛216 = 6
So, 216√3 is equal to 6√3. Now, we need to find the value of 6√3.
To evaluate this, we can split √3 into √(3 * 1), which can be simplified as follows:
6√(3 * 1) = 6√3 * √1
Since the square root of 1 is 1, we can simplify further:
6√(3 * 1) = 6√3 * 1 = 6√3
Therefore, 216√3 is equal to 6√3.
So, the correct answer is 6.