Question 128032
Squaring a number is multiplying it by itself.  2 squared is 2 X 2 is 4, for example.  The square root is just the opposite of that.  If I want the square root of a number, find a number when multiplied by itself gives the original number.  So if I want the square root of 9, I know that 3 X 3 is 9, so 3 is the square root of 9.  But 3 is only one of the square roots of 9, because -3 X -3 is also 9.


As for notation, if you see {{{sqrt(9)}}}, then by convention, the positive square root is meant.  So {{{sqrt(9)=3}}} is a true statement.  But if the problem is {{{x^2=9}}}, you must consider both the positive and negative values for x that would make the statement true.  In this case, {{{x=3}}} or {{{x=-3}}}


Let's look at your example problem:  {{{2x^2=36}}}


First step is to divide both sides by 2:  {{{x^2=18}}}


Now we can take the square root of both sides of the equation:  {{{x=sqrt(18)}}} or {{{x=-sqrt(18)}}}


But we aren't quite done yet.  One of the rules for square roots says:


{{{sqrt(ab)=sqrt(a)*sqrt(b)}}}.


Now we know that {{{18=2*9}}}, so we can write our earlier answer as:


{{{x=sqrt(9)*sqrt(2)}}} or {{{x=-sqrt(9)sqrt(2)}}}, but remember {{{sqrt(9)=3}}}, so the final result is:


{{{x=3*sqrt(2)}}} or {{{x=-3*sqrt(2)}}}


That's as far as you can go without making an approximation since {{{sqrt(2)}}} is irrational, meaning that it cannot be expressed exactly as a decimal.