Simplifying Radicals and ExponentsDate: 9/3/95 at 11:23:20 From: Richard Seguin Subject: Help on "Developing Operations: Radicals" In my math book I have a question like this: ____ A 1) Which of the following Radicals are equivalant to \/ 32 IT gives me these choices: ___ ____ _____ _____ _____ 3\/16 , -2\/ 8 , 4\/ 2 , 2\/ 64 , 3\/ 320 _____ Could you please explain why and how these can be equal to \/ 32 The other thing I had a problem with was this question: a) 2^1/4 if this doesn't look right it's supposed to be this 2 TO THE POWER OF 1/4 How do you get that low of a answer? Richard Seguin Date: 9/4/95 at 16:2:34 From: Doctor Ethan Subject: Re: Help on Hey Richard, These are neat questions. I hope that my explanations make sense to you. 1. To get this we have to understand a little about radicals. Here are a few rules that you need to know. I am going to write them using variables to show that they are good for any numbers. _______ _ _ _ _ \/a*b*c*d = \/a * \/b * \/c * \/d The next rule follows from it. _____ _ \/a^2*b = a\/b _____ ___ _ _ _ I got this by \/a^2*b = \/a^2 * \/b = a * \/b = a\/b Now using these rules lets look at problem 1. __ __ _ _ _ \/32 = \/16 * \/2 = 4 * \/2 = 4\/2 __ __ Now you try \/27 and \/18 which work the same way. For your second question, I guess I have less to say. I understand 2^1/4 just fine but I can't really tell you much about it. If you want a decimal approximation, I can give you that. It is 1.18920711500272106672 Other than that there isn't much to say. 2^1/4 is the number that when taken to the fourth power, equals two. There really isn't much more. -Doctor Ethan, The Geometry Forum Date: 9/5/95 at 5:47:16 From: Richard Seguin Subject: Re: Help on >Okay now for your second question I guess I have less to say. > >I understand 2^1/4 just fine but I can't really tell you much about it. > >If you want a decimal approximation , I can give you that. > >It is 1.18920711500272106672 > >Other than that there isn't much to say > >2^1/4 is the number that when taken to the fourth power, equals two. > >There really isn't much more. Well how did you come to this answer. I know what it comes to but how did you come across a answer like that? It couldn't have been from memory right? Richard Seguin Date: 9/13/95 at 15:15:38 From: Doctor Ethan Subject: Re: Help on You are right it definitely wasn't from memory. I actually got the answer from a computer. But here is another way to think about it that would allow you to use a calulator or pencil and paper to get the answer. 2^(1/4) squared is 2^1/2 Do you know why? Well, 2^1/2 is 1.414028...... (that is from memory but it is really close to that). So now to find 2^1/4 we just need to take the square root of 1.414028 Or if we are starting from 2 we can just take the square root twice and get the fourth root of 2 or 2^1/4 Hope that explains it a little. Maybe you feel like it is cheating to just say use a calculator to take the square root. If you feel that way, there are ways to approximate square roots by hand, but they are not fun so I would just get comfortable with a calculator. -Doctor Ethan, The Geometry Forum Date: 9/14/95 at 17:10:48 From: Doctor Ken Subject: Re: Help on Richard - Let me just add to what Ethan told you. If you have a number to the 1/n power, that's the same as the nth root of that number. So something like 5^(1/7) is the 7th root of 5. So if you have any number to the p/q power, that's the same as the pth power of the qth root of the number: thus 8^(2/3) = 4. Why? Because if you multiply x^(1/n) times itself n times, you get x. Therefore it must be the nth root of x. - Doctor Ken, The Geometry Forum |
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