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  1. Had we would have taken the original square root instead of Principal Square root, our extraneous solution might/would have worked"

  2. If we would have taken the original square root instead of Principal Square root, our extraneous solution might/would have worked.

Is there any difference between those two sentences?

If any, when should we use one over the other?

[UPDATE] I'm not a native English speaker and I used google translator and both of the sentences showed the same result.

I tried to use Ginger to check if there is any grammatical mistake, there wasn't any.

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    "Had we would have" just sounds weird. – Hot Licks Nov 26 '19 at 1:54
  • Ikr, but I can't really recall where I heard it the last time, but I'm sure I did. Thus the confusion! – Daksh Gargas Nov 26 '19 at 2:00
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    "Had we would have taken" is ungrammatical. What about "Had we taken... ...our results would have been..." – Centaurus Nov 26 '19 at 2:04
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    The difference is that the second one is common in American English, but considered ungrammatical by many educated people, and the first one is considered ungrammatical by nearly everyone. – Peter Shor Nov 26 '19 at 3:03
  • A conditional clause can be introduced either by "Had" or "If". – Ravi Shankar Jaipuriar Nov 26 '19 at 4:59
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Both are ungrammatical, so the difference is moot.

The right form is, "Had we taken the original square root...."

or

"If we had taken the original square root...."

"Done the square root" is weak.

It's not a rule these days, but an if (or had) clause should be followed by a then clause.

If we had taken the original square root...then our extraneous solution might/would have worked.

Formal logic and math use if...then for conditional statements, and I think the pairing works well in ordinary writing, too. Again, not a rule but a good habit.

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