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    rchlclairelove's Avatar
    rchlclairelove Posts: 1, Reputation: 1
    New Member
    		  
    #1

    Feb 12, 2009, 05:59 PM
    Simpifying dividing and mult. Radicals
    I can't for the life of me figure out the sqare root of 75.
    bones252100's Avatar
    bones252100 Posts: 253, Reputation: 29
    Full Member
    		  
    #2

    Feb 12, 2009, 06:14 PM
    8.660254
    rwinterton's Avatar
    rwinterton Posts: 289, Reputation: 15
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    #3

    Feb 13, 2009, 06:33 AM
    It's an irrational number. There is no exact square root of 75.

    Approximately:

    8.6602540378443864676372317075294

    To 32 digits (Windows Calculator)
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
    Uber Member
    		  
    #4

    Feb 13, 2009, 07:14 AM
    Quote Originally Posted by rchlclairelove View Post
    i can't for the life of me figure out the sqare root of 75.
    How are you expected to work it out?
    rwinterton's Avatar
    rwinterton Posts: 289, Reputation: 15
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    #5

    Feb 13, 2009, 07:49 AM
    There are a couple of different algorithms. The simplest one (the one that is used for computers), you take a guess:

    1. Given: N (75 in this case)
    2. Guess: 8.5 (because 8*8 is 64 and 9*9 is 81)

    3. Divide 75 by 8.5 = 8.8235
    4. Average the guess with the dividend in #3 (8.5 + 8.8235) / 2 = 8.66176
    5. Use the value obtained in #4 as the new divisor (the new guess) in item #3. (75 / 8.66176 = 8.65874).

    repeat until the averaged value is the same as the guess within the desired accuracy.

    The second algorithm seems more complicated -- but I learned it in junior high school. I started to describe it and realized that I'd need a lot more space and time to describe it in a manner that would be understood. I then googled this link.

    http://www.homeschoolmath.net/teachi...-algorithm.php

    If you really want to know this algorithm, look at this link.

    Here's another example.

    http://www.homeschoolmath.net/teachi...hm-example.php
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #6

    Feb 14, 2009, 02:22 PM
    To simplify try:



    Now, multiply the square root of 3 b by 5.
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