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August 1st, 2007, 02:28 PM  #1 
Newbie Joined: Aug 2007 Posts: 1 Thanks: 0  Square roots question
What is the square root of 19 to the nearest whole number? What is the square root of 171 to the nearest whole number? Solve F to the second power = 169 is square root of 36 rational, irrational, interger rational, or other? estimate b to the 2nd power = 525 to the nearest integer. square root of 17 to nearest tenth. square root of negative 102 round to the nearest tenth.. thanks.. if these could be answered by today that would help out and everything. 
August 1st, 2007, 04:30 PM  #2 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  let us assume that we can't use any calculator related tools, and let us solve it both algebraically and in calculus terms. Q. What is the square root of 19 to the nearest whole number? A. let us assume that newton's method will help us solve this. let f(x)=x^219=0, where we want to find for x, approximation. take the derivative of f(x).. which gives us f'(x)=2x. let us assume that x_0=4, and x_1=5. let's use the linear approximation, using general equation f(x)=l(x)=f(x_k)+f'(x_k)(xx_k), where k is the kth term of x. let's use x_0=4 first. f(x)=l(x)=f(4)+f'(4)(x4)=3+8(x4)=8x35=0 8x=35 x=35/8=4.375 is an example of an close approximation. let's use the x_1=5 for our final approximation. f(x)=l(x)=f(5)+f'(5)(x5)=6+10(x5)=10x44=0 10x=44 x=44/10=22/5=4.4 is an another example of an close approximation. since the 4.375 is an approximation for x_0=4, and 4.4 is an approximation for x_1=5, and x=sqrt(19) must be between those two approximations, we can say that nearest whole number for sqrt(19) is 4. do this the same way for your second problem, third problem, fifth, sixth and seventh problem. since sqrt(36)=6, we can say that it's "positive, integer, rational, even, natural, composite number". 
August 11th, 2007, 09:40 AM  #3  
Global Moderator Joined: Dec 2006 Posts: 21,029 Thanks: 2259  Quote:
What is your answer for the third problem? Also, do you really do things exactly the same way for the seventh problem?  
August 11th, 2007, 12:44 PM  #4  
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Quote:
 
August 11th, 2007, 02:27 PM  #5  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Help.. Please
I did some mental math to give pointers to the answers. Quote:
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August 12th, 2007, 03:25 PM  #6  
Senior Member Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0  Re: Help.. Please Quote:
Over the set of complex numbers, the answer would be ±10.01i, where i:=√1.  
August 13th, 2007, 07:54 AM  #7  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Help.. Please Quote:
 
August 13th, 2007, 08:40 AM  #8 
Senior Member Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0 
I suppose you can stil define square root as a function over complex numbers. The difficulty arises in odd roots, where the most natural definition over complex numbers disagrees with the most natural definition over real numbers when you examine the negative reals. For example, when dealing with roots of complex numbers, the most natural definition for the cube root of 1 (if you insist on making cube root a function) is cbrt(e^(pi*i))=e^(pi*i/3)=1/2+sqrt(3)*i/2, where as, over the set of reals, the only candidate for the cube root of 1 is 1. That is why I think it makes more sense to, once you start dealing with complex numbers, let nth root be multivalued (specifically, it has n values, as long as n is an integer). 
August 13th, 2007, 08:47 AM  #9  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
But yes, if it's multivalued you should have two answers, and if the range is defined as the reals you should have zero. Maybe the teacher should tell students how many answers to give...  

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