SOLUTION: what the square root of 75 in complete form (showing how you got the answer)

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Question 390827: what the square root of 75 in complete form (showing how you got the answer)
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
75 in factored form is 5%5E2+%2A+3. Therefore, sqrt%2875%29+=+sqrt%285%5E2+%2A+3%29. Since sqrt%28ab%29+=+sqrt%28a%29sqrt%28b%29 for real numbers a,b (not complex numbers), then sqrt%285%5E2+%2A+3%29+=+sqrt%285%5E2%29sqrt%283%29+=+5sqrt%283%29.

It doesn't necessarily work for complex numbers because

sqrt%28-1%29sqrt%28-1%29+=+i%2Ai+=+-1 and if sqrt%28-1%29sqrt%28-1%29+=+sqrt%28%28-1%29%28-1%29%29+=+sqrt%281%29+=+1, then -1 = 1 and we have a contradiction.