Question 114337
A square root of a number is another number, when multiplied by itself results in the original number.  2 is a square root of 4, for example.  The thing is, whenever you take a square root, you need to consider both the positive and the negative, because -2 is also a square root of 4.


So let's look at your problem:


{{{(x+8)^2=81}}}


The first thing you need to do is take the square root of both sides of the equation.  Beginning with the left side of the equation, remember that {{{sqrt(a^2)=a}}} for any real number a.  On the right side of the equation, ask yourself, what number when multiplied by itself equals 81?  I sincerely hope you came up with both 9 and -9.


So now we can re-write the equation like this:


{{{sqrt((x+8)^2)=sqrt(81)}}} or
{{{sqrt((x+8)^2)=-sqrt(81)}}}


{{{x+8=9}}} or {{{x+8=-9}}}


{{{x=1}}} or {{{x=-17}}}


Let's check to see if the answers make the original statement true:


{{{(1+8)^2=81}}} => {{{9^2=81}}}, so that answer checks
{{{(-17+8)^2=81}}} => {{{(-9)^2=81}}} so that answer checks as well.


If you are confused at all about the fact that there are two answers, don't worry.  Having two answers for a 2nd-degree equation (one that has an {{{x^2}}} or {{{xy}}} term in it) is part of the great and wonderful pattern of mathematics.  You'll discover later on that 3rd-degree equations, such as things with an {{{x^3}}} in them will have THREE solutions or roots.  In fact, the fundamental theorem of algebra tells us that an n-th degree equation has n roots.  For the time being, have faith.  It will all make good sense in the end.


Hope that helps,
John