My Math Forum "easy" question involving a surd

 Algebra Pre-Algebra and Basic Algebra Math Forum

 August 3rd, 2013, 11:31 PM #1 Newbie   Joined: Aug 2013 Posts: 4 Thanks: 0 "easy" question involving a surd Hi, I hate to ask this as I'm sure it has a really, really very easy solution, but I simply cannot get my head around this. I have a question as follows: Write as a surd in it's lowest form:   ____1____      5 - ?3 Every other question from this source was ridiculously easy, so this is killing me to have to ask. I'd love an explanation rather than a simple answer if anyone has the time. Many thanks!
 August 4th, 2013, 12:20 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: "easy" question involving a surd We are given: $\frac{1}{5-\sqrt{3}}$ What you want to do is multiply this with $1=\frac{5+\sqrt{3}}{5+\sqrt{3}}$ to get: $\frac{1}{5-\sqrt{3}}\cdot\frac{5+\sqrt{3}}{5+\sqrt{3}}=\frac{ 5+\sqrt{3}}{25-3}=\frac{5}{22}+\frac{1}{22}\sqrt{3}$
 August 4th, 2013, 03:12 AM #3 Newbie   Joined: Aug 2013 Posts: 4 Thanks: 0 Re: "easy" question involving a surd Great, thanks Mark. I do feel like a fool for falling for it. My logical brain kept telling me it was as straight-forward as that, but I was convinced I should have had a cleaner answer... I had originally come up with the following: __5 + ?3__       22 It just didn't look right to me as all the other answers were simple x?y format surds. I guess it was just a successful 'curveball'. Is it correct to format it as I have done? Many thanks for the help!
 August 4th, 2013, 03:16 AM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: "easy" question involving a surd I actually prefer it the way you have formatted it, but some teachers prefer the format $a+b\sqrt{c}$ for quadratic surds.
 August 4th, 2013, 03:44 AM #5 Newbie   Joined: Aug 2013 Posts: 4 Thanks: 0 Re: "easy" question involving a surd Ah, I just realised that I've put this in the wrong place in my haste in posting. I'm not sure if it isn't really suitable for here, I really do not know the school system structure in the USA and just looked up Middle School and Elementary School. I can't remember if I did surds back then, certainly not in my equivalent of elementary school! Please move it to a more suitable subforum if you will, and sorry for making a blunder of my first posts. I am a lot older than you probably assumed! The reason I was quite embarrassed by my question is that we are doing far more complicated work and yet I was tripped up by this revision...
 August 4th, 2013, 03:49 AM #6 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: "easy" question involving a surd I try not to make assumptions about the age of people based on the level of work they are posting...we have a middle-schooler doing university and graduate level work and we get senior citizens doing pre-algebra. I did move your topic though, and we certainly do not consider this a blunder...sometimes it is not so obvious where to post. Welcome to MMF, by the way!
 August 4th, 2013, 04:00 AM #7 Newbie   Joined: Aug 2013 Posts: 4 Thanks: 0 Re: "easy" question involving a surd Thanks, hopefully I'll be more careful next time. I'm bound to have have more silly questions! Somehow I managed to keep away from maths forums until now, but I'm hooked already!

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