This article assumes that the reader is familiar with multiplying radicals. If necessary, see my article here<\/a> about that.<\/p>\n Rationalizing the denominator is done when there’s a radical on the bottom of a fraction.\u00a0 Consider the following:<\/p>\n \u00a0 Solution:<\/p>\n To rationalize the denominator, you multiply the top and bottom by the same number. The number is chosen so it turns the radical on the bottom into a whole number:<\/p>\n 7\/(2√(3))*√(3)\/√(3)=7√(3)\/(2√(3)√(3))<\/p>\n Above, we have multiplied 7\/(2√(3)), top and bottom, by √(3). We can do so because when you multiply the top and bottom by the same amount, the fraction’s value doesn’t change, just its form. Notice that √(3)√(3)=3. Therefore,<\/p>\n 7\/(2√(3))*√(3)\/√(3)=7√(3)\/(2√(3)√(3))=7√(3)\/(2*3)=7√(3)\/6<\/p>\n So it turns out that, when you rationalize the denominator,7\/(2√(3)) becomes 7√(3)\/6<\/p>\n Of course, there are more complicated situations where you have to rationalize the denominator. I’ll get to them in future posts:)<\/p>\n
\nExample 1:<\/strong> Simplify 7\/(2√(3))<\/p>\n