To reduce the radical of 216, we can start by factoring the number into its prime factors. We can do this step by step.
Step 1: Prime factorize 216
216 can be written as the product of its prime factors: 2, 2, 2, 3, and 3. So we can write 216 as 2^3 * 3^3.
Step 2: Group the factors into pairs
To reduce the radical, we look for pairs of the same prime factors. In this case, there are two pairs of 2s and one pair of 3s. We can now rewrite 216 as the product of the pairs: (2 * 2) * (2 * 2) * (3 * 3). Simplifying this further, we get 4 * 4 * 9.
Step 3: Write the perfect squares outside the radical
Now, we write the perfect squares outside the square root symbol. The perfect squares are the numbers that can be squared to give the original number. In this case, the perfect squares are 4 (2 * 2) and 9 (3 * 3).
So, the square root of 216 can be expressed as the product of the square root of the perfect squares and any remaining factors inside the radical. Therefore, the square root of 216 is equal to 2 * 2 * 3 * the square root of 6.
Final answer: 2 * 2 * 3 * √6