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Math Help - Finding the root of 75

  1. #1
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    Finding the root of 75

    I have been told that in order to find the root of 75 you need to factor it
    and then do 5 times root of 3 or something like that
    anyway why cant i just break 75 into 2 times 35 and so on?
    in any case in simple terms can you explain it?
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  2. #2
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    Re: Finding the root of 75

    Quote Originally Posted by ariel32 View Post
    I have been told that in order to find the root of 75 you need to factor it
    and then do 5 times root of 3 or something like that
    anyway why cant i just break 75 into 2 times 35 and so on?
    in any case in simple terms can you explain it?
    1. You can easily calculate the square-root of a number if this number is a square: \sqrt{9} = 3~or~\sqrt{\frac4{25}}=\frac25

    2. If the number is not a square (75 is not a square of a rational number) you can express \sqrt{75} as an approximation in decimal form. You have then a result with a lot of digits - and it is still not accurat!

    Therefore you try to split a number into a product of a square (the square should be as large as possible) and another rational number. So you are able to calculate the square-root at least from the square. The other number remains under the root sign.

    Example:

    \sqrt{128} = \sqrt{4 \cdot 32} = \sqrt{16 \cdot 8} = \sqrt{64 \cdot 2}

    Since 64 is the greatest square you'll get \sqrt{128} = 8 \cdot \sqrt{2}
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  3. #3
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    Re: Finding the root of 75

    \sqrt{75}=\sqrt{3\cdot5\cdot 5}
    \sqrt{3\cdot5^{2}}
    5\sqrt{3}
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  4. #4
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    Re: Finding the root of 75

    Rewrite each as a multiple of a square:
    √(25 * 3)
    √25 * √3
    5√3
    Thanks from DIOGYK
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