Question 218853
There are easy and a not-so-easy ways to solve this. But either way we do this we have to understand enough about exponents to know that {{{x^(1/2)*x^(1/2) = (x^(1/2))^2 = x}}}<br>
The easy way is found by recognizing that
{{{( a^(1/2) + b^( 1/2 ))( a^( 1/2) - b^( 1/2 ))}}}
fits the pattern:
{{{p+q)(p-q) = p^2 - q^2}}} with {{{p = a^(1/2)}}} and {{{q = b^(1/2)}}}. So
{{{( a^(1/2) + b^( 1/2 ))( a^( 1/2) - b^( 1/2 )) = (a^(1/2))^2 - (b^(1/2))^2 = a-b}}}
The harder way is to multiply {{{( a^(1/2) + b^( 1/2 ))( a^( 1/2) - b^( 1/2))}}}. Multiplying expressions like this is done using something that is often called FOIL (First, Outside, Inside, Last):
{{{( a^(1/2) + b^( 1/2 ))( a^( 1/2) - b^( 1/2 )) = a^(1/2)*a^(1/2) - a^(1/2)*b^(1/2) + a^(1/2)b^(1/2) - b^(1/2)*b^(1/2) = a - b}}}