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
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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.
To reduce the radical √216, follow these steps:
Step 1: Identify the factors of 216. The factors of 216 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
Step 2: Find the largest perfect square factor of 216. In this case, the largest perfect square factor of 216 is 36.
Step 3: Express the number 216 as the product of the perfect square factor and the remaining factor. 216 can be expressed as 36 * 6.
Step 4: Rewrite the square root of 216 using the perfect square factor outside the square root symbol. The square root of 216 can be written as √(36 * 6).
Step 5: Simplify the expression inside the square root symbol. Since 36 is a perfect square, we can take its square root and leave it outside the square root symbol. Simplifying further, we have √(36) * √(6) = 6 * √(6).
Therefore, the radical √216 can be reduced to 6√6.
To reduce the radical, we need to find perfect square factors of the number under the radical sign. Let's go step by step to reduce the square root of 216.
Step 1: Split 216 into its prime factorization:
216 = 2 * 2 * 2 * 3 * 3 * 3
Step 2: Group the prime factors in pairs and take out the pairs that have even exponents:
216 = 2^3 * 3^3
Step 3: Rewrite the pairs with even exponents outside the square root, and the remaining factors inside the square root:
√(2^3 * 3^3)
Step 4: Simplify the expression inside the square root:
√(8 * 27)
Step 5: Simplify further by finding perfect square factors inside the square root:
√(4 * 2 * 9 * 3)
Step 6: Take out the perfect square factors outside the square root:
2 * 3 * √(2 * 3)
Step 7: Multiply the numbers outside the square root:
6 * √(2 * 3)
Therefore, the reduced form of the square root of 216 is 6√(6).
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
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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.