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

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**

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.

**Attribution***Source : Link , Question Author : Daksh Gargas , Answer Author : Community*