\nThe following is by my understanding.<\/p>\n
\nWay back in my post from Mar 22, 2014,<\/a> I began about rationalizing the denominator. However, there is a more complicated scenario, as follows:<\/p>\n \nExample: rationalize the denominator of (3√2)\/(1-2√5)<\/p>\n Solution:<\/p>\n \nIn a case like this, one has to multiply both numerator and denominator by the conjugate of the denominator. (See my post from Jul 27, 2026<\/a> about the conjugate.)<\/p>\n \nThe conjugate of the denominator is 1+2√5, so we get<\/p>\n \n[(3√2)(1+2√5)]\/[(1-2√5)(1+2√5)]<\/p>\n \nBy FOIL (see see my post from Nov 26, 2012<\/a> about the foil method),<\/p>\n \n(1-2√5)(1+2√5) = 1+2√5-2√5-4(√5)^2 = 1-4*5 = 1-20 = -19<\/p>\n \nMeanwhile the numerator becomes<\/p>\n \n3√2(1+2√5) = 3√2+6√(10)<\/p>\n \nSo we arrive at<\/p>\n-(3√2 + 6√(10))\/19<\/p>\n \nRationalizing the denominator doesn’t necessarily get rid of a mess; it just rewrites the expression with the radicals out of the denominator.<\/p>\n \nHand-held calculators that can do this, and show the answer symbolically, have been available for around twenty years.<\/p>\n \nSource:<\/p>\n \nTraverse, K.J., Dalton, L.C., Brunner, V.F., Taylor, A.R. (1977). Using Advanced Algebra.<\/em> Doubleday Canada Limited.<\/p>\nJack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.\n\n\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" Tutoring math, you deal with this topic for high school and calculus. The tutor continues with …<\/p>\n