I’ve written a number of articles on simplifying radicals. I won’t encumber this one with a list of the previous ones, but you can find them by searching for “radical” or “root” in the search box.<\/p>\n
Today, we’ll look at this example. (Note that the fifth root is the same as the exponent 1\/5.)<\/p>\n
Simplify<\/strong> (-486)^(1\/5)<\/p>\n Note that you can simplify odd roots of negatives, just not even ones.<\/p>\n If you try to take the fifth root of -486 on your calculator, you’ll get a messy decimal, which is not acceptable as simplified form. Therefore, a perfect fifth power number must lurk inside -486; the job is to find it.<\/p>\n We start by listing perfect fifth powers:<\/p>\n 2^5=32 Clearly, 4^5 is much too large to fit in -486; therefore, our number must be either 32 or 243. 32 looks tempting, by if you try -486\/32 you get a decimal. However,<\/p>\n -486\/243=-2<\/p>\n Therefore,<\/p>\n (-486)^(1\/5) = (-243)^(1\/5)*(2)^(1\/5) = -3*(2)^(1\/5)<\/p>\n When simplifying an odd root of a negative, always take the negative out front:)<\/p>\n
\n3^5=243
\n4^5=1024<\/p>\n