Is there any difference between 'Had we would have' and 'If we would have'?

Question

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.

Answer 1

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.