tag:blogger.com,1999:blog-7718462793516968883.post8694847598401872994..comments2021-01-05T07:04:40.286-05:00Comments on MadMath: Reading RadicalsDeltahttp://www.blogger.com/profile/00705402326320853684noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-7718462793516968883.post-54772266810522661412016-04-16T01:08:23.085-04:002016-04-16T01:08:23.085-04:00Here's the distinction, which I overly abbrevi...Here's the distinction, which I overly abbreviated in the main blog: <i>the radical can still be simplified</i>. That is: while -x is the simplest way to write that expression, √x is usually not (e.g., in the cases of √9 or √45), and it's the only apparently unary operator where that's the case. In other words: from the students' perspective, the radical is the only basic operator where you can "do something" to it (simplify it) without any 2nd parameter in sight (due to the default index of 2). <br /><br />Thanks for helping me to clarify that point. Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-57028684166509486822016-04-15T05:11:22.399-04:002016-04-15T05:11:22.399-04:00I don't see the distinction. If we interpret n...I don't see the distinction. If we interpret negation and subtraction as completely different operations, even though they use the same symbol and negation is syntactically identical to subtraction with an omitted zero, then why can't we do the same with radicals?Don Rebahttps://www.blogger.com/profile/18015532040220223370noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-57179065866465950052016-04-12T11:28:43.937-04:002016-04-12T11:28:43.937-04:00That's a great point, to avoid rewriting all t...That's a great point, to avoid rewriting all the book exercises.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-14452497862030645702016-04-12T11:28:20.065-04:002016-04-12T11:28:20.065-04:00Thanks for the vote of support!Thanks for the vote of support!Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-5511881052891167832016-04-12T01:04:31.710-04:002016-04-12T01:04:31.710-04:00I think you ought to try it. You'll run into s...I think you ought to try it. You'll run into some friction because none of the textbooks will have the "implicit 2" written in, but it would probably be a good re-inforcement for the students to explicitly write the 2 for all their assignments. That is, whenever they see the radical without the 2, they should transcribe it in their homework with the 2.Barry Brownhttps://www.blogger.com/profile/08997958644859140599noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-42325393435364328602016-04-11T15:55:31.248-04:002016-04-11T15:55:31.248-04:00It's worth trying. And I'll be interested ...It's worth trying. And I'll be interested in your results. I often talk about the "invisible two" sitting there. (As I talk about the "invisible 1" as the co-efficient of a variable sometimes.)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-29503471531165673762016-04-11T11:02:26.047-04:002016-04-11T11:02:26.047-04:00But the expression -x would usually not be defined...But the expression -x would usually not be defined as a subtraction. <br /><br />Regardless of how we interpret square roots, it's a notational outlier, it's confusing to students, and it clashes with the notation for higher roots and all other elementary operations (especially including its inverse, the squaring function). Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-6039686599925168062016-04-11T05:41:24.963-04:002016-04-11T05:41:24.963-04:00In the operation 0-x, 0 may be omitted. Or else yo...In the operation 0-x, 0 may be omitted. Or else you could consider the square root a unary operation.Don Rebahttps://www.blogger.com/profile/18015532040220223370noreply@blogger.com