Question 719087
{{{(sqrt(3) + sqrt(5))(sqrt(3) + sqrt(5))}}}
Don't let the square roots distract you. This is one two-term expression times another two-term expression. You can use FOIL to multiply them.<br>
But if we look closer, the two two-term expressions are exactly the same. We could rewrite the expression as:
{{{(sqrt(3) + sqrt(5))^2}}}
So not only can we use FOIL we can use a factoring pattern:
{{{(a+b)^2 = a^2+2ab+b^2}}}
to multiply. Using the pattern is faster and easier than FOIL so I will use the pattern. In our expression, our "a" is {{{sqrt(3)}}} and our "b" is {{{sqrt(5)}}}. So according to the pattern
{{{(sqrt(3) + sqrt(5))^2}}}
will be equal to
{{{(sqrt(3))^2 + 2*sqrt(3)*sqrt(5)+ (sqrt(5))^2}}}
Simplifying...
{{{3 + 2*sqrt(15)+ 5}}}
{{{8 + 2*sqrt(15)}}}
This is the answer. (If you had used FOIL correctly you would have gotten the same thing.)