Expert: Sherry Wallin - 7/16/2011

Question
{(7*3^1/2)/ (10^1/2+3^1/2)} – {(2*5^1/2)/ (6^1/2+5^1/2)} – {(3*2^1/2)/ (15^1/2+ [3*2^1/2])}

Answer
Sri~

Multiply each term by the conjugate of it's denominator.

For example the first term's denominator is 10^(1/2) + 3^(1/2) so it's conjugate is 10^(1/2) - 3^(1/2). the interesting thing about multiplying a binomial by it's conjugate is that you get rid of the middle terms and thus you will also get rid of the radicals. You will need to also multiply the numerator by the denominators conjugate as well.

first term: (7*3^1/2)(10^1/2-3^1/2) (10^1/2+3^1/2(10^1/2-3^1/2) = 3^(1/2)[(10^(1/2)-3^(1/2)]

do the same for the other two terms and you will get -2*5^(1/2)[(6^(1/2)-5^(1/2)] and 2^(1/2)[(15^(1/2)-3*2^(1/2)]

Now multiply and  combine like terms

30^(1/2) - 3 - 2*30^(1/2) + 10 + 30^(1/2) - 6 = 1

Math Prof