Write square root of, minus, 216, end square root −216 in simplest radical form.
Question
Write square root of, minus, 216, end square root in simplest radical form.
Solution
The square root of a negative number involves the concept of imaginary numbers. The square root of -1 is represented as 'i'.
So, to find the square root of -216, we first find the square root of 216, which is 14.7 (approximately), and then multiply it by 'i'.
Therefore, the square root of -216 is approximately 14.7i.
However, if you want to express it in simplest radical form, you would first break down 216 into its prime factors. The prime factorization of 216 is 22233*3.
Pairing these factors into two, we get three pairs: (2,2), (2,3), and (3,3). The square root of each pair is 2, 2, and 3 respectively.
So, the square root of 216 is 223 = 12.
Therefore, the square root of -216 in simplest radical form is 12i.
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