Question

Go step by step to reduce the radical.
square root of, 216, end square root
216
​

square root of, empty space, end square root
x
​

square root of, empty space, end square root
x
​

Answer 1

To reduce the square root of 216, we can break down 216 into its prime factors:

216 = 2 × 2 × 2 × 3 × 3 × 3

Now, we pair up the prime factors into groups where each group has two of the same factors:

216 = 2 × 2 × (2 × 3) × (3 × 3)

We can rewrite this expression as:

216 = (2 × 2 × 3 × 3) × (2 × 3)

Square roots simplify by taking out pairs of the same factor and leaving one of each outside of the square root sign.

So, taking out pairs of 2 and 3, we simplify the expression:

√216 = √[(2 × 2 × 3 × 3) × (2 × 3)]

√216 = (2 × 3) × √[(2 × 3)]

√216 = 6 × √(2 × 3)

Finally, we can simplify the expression further by multiplying the numbers outside of the square root:

√216 = 6√6

Thus, the square root of 216 is equal to 6√6.

Answer 2

Go step by step to reduce the radical.
square root of, 216, end square root
216
​

square root of, empty space, end square root
x
​

square root of, empty space, end square root
x
​

Answer
Attempt 1 out of 2
You must answer all questions above in order to submit.

Answer 3

To reduce the radical, let's go step by step to simplify the square root of 216.

Step 1: Find the prime factorization of 216:
216 can be written as 2 × 2 × 2 × 3 × 3 × 3.

Step 2: Group the prime factors in pairs of the same number:
(2 × 2) × (2 × 3) × (3 × 3).

Step 3: Take out the pairs of the same number outside the square root:
2 × 3 × 3.

Step 4: Simplify the expression inside the square root:
√(2 × 3 × 3).

Step 5: Multiply the numbers outside the square root:
6.

Therefore, the simplified form of the square root of 216 is 6√(2 × 3) or simply 6√6.