# Algebra II b

rationalize the denominator and then simplify 5/2+~3

### Comments for Algebra II b

 Mar 02, 2011 Algebra II b by: Staff The question: rationalize the denominator and then simplify 5/2+~3The answer:5/[2+sqrt(3)]The square root sign in the denominator will disappear if we apply the difference of squares formula.The difference of squares formula states that:(a + b)(a − b) = a² − b²Therefore, if we could multiply the denominator by its conjugate [which is 2-sqrt(3)], the result would contain no square root sign. The denominator would simply = 1:[2+sqrt(3)]*[2-sqrt(3)] = 2² − [sqrt(3)]²= 4 - 3= 1 However, in order to preserve the value of the original fraction, both the numerator and denominator must each be multiplied by the same amount: [2-sqrt(3)].5/[2+sqrt(3)] must be multiplied by the faction [2-sqrt(3)]/[2-sqrt(3)].Note that: [2-sqrt(3)]/[2-sqrt(3)] = 1{5/[2+sqrt(3)]}*1 = {5/[2+sqrt(3)]}*{[2-sqrt(3)]/[2-sqrt(3)]}= {5*[2-sqrt(3)]}/{[2+sqrt(3)]*[2-sqrt(3)]}= {5*[2-sqrt(3)]}/{2² − [sqrt(3)]²}= {5*[2-sqrt(3)]}/1= 5*[2-sqrt(3)]= 10 - 5*sqrt(3)The final answer is: 10 - 5*sqrt(3)Thanks for writing.Staff www.solving-math-problems.com