Question 711991
There are a few problems with what you posted:<ul><li><i>Every</i> equation you posted is ambiguous. None of them make clear what is inside the square root. For example, the first equation could be any of the following:
{{{sqrt(3)x=sqrt(x)+6}}}
{{{sqrt(3x)=sqrt(x)+6}}}
{{{sqrt(3)x=sqrt(x+6)}}}
{{{sqrt(3x)=sqrt(x+6)}}}
You have parentheses around the words "square root". Putting parentheses around the radicand (the expression within a radical is called a radicand) is much more important.</li><li>I don't think "extraneous equations" is a meaningful phrase. Solving square root equations like these can result in what are called "extraneous solutions".</li></ul>Please re-post your question using parentheses to make the equations unambiguous.