SOLUTION: Why does {{{sqrt(3x)}}}{{{""=""}}}{{{-6}}} not have a real solution?

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Question 358464: Why does sqrt%283x%29%27%27=%27%27-6 not have a real solution?
Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(8908) About Me  (Show Source):
You can put this solution on YOUR website!
Because when written with a radical Ö a square
root or a 4th root root%284%2C%27+%27%29, or a 6th root root%286%2C%27+%27%29, 8th root
root%288%2C%27+%27%29, or any root with an EVEN index can never represent a negative
number (that's not true with odd index roots).

Therefore your equation

sqrt%283x%29%27%27=%27%27-6

has a square root written with a radical on the left, which means that
the left side is NOT negative.  Yet it is equal to a negative number on
the right,  which means it can have no real solution.

Edwin


Answer by Alan3354(30993) About Me  (Show Source):
You can put this solution on YOUR website!
Why does sqrt%283x%29%27%27=%27%27-6 not have a real solution?
----------------
sqrt%283x%29+=+-6
Square both sides
3x = 36
x = 12
------
Check:
sqrt%283%2A12%29+=+sqrt%2836%29
= +6, -6