8
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The answer is 64. The cube-root of 512 is 8, 8 squared is 64.
square root of 8
The original number - the number you take the square root of - is somewhere between 8 squared (8 x 8) and 9 squared (9 x 9).
The square root of minus 8 is equal to the square root of 8 times the square root of minus 1, or 2.8284i.
Trial and error. You know that the answer will be between 2 and 3, closer to 3. 2.8 squared = 7.84 2.82 squared = 7.95 2.828 squared = 7.99 2.8284 squared = 7.999 which is close enough for me.