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Math Help - Radicals

  1. #1
    Junior Member Sammyj's Avatar
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    Radicals

    Simplify the expressions

    1) 2 ^3 sq rt 5 - 4 ^3 sq rt 40 + 3 ^3 sq rt 135


    2) sq rt p^7 q^3 - sq rt p^5 q^9 + sq rt p^9 q

    3) sq rt b^3 * ^4 sq rt b^3

    4) sq rt 16 - 8x + x^2

    I am completely lost I try researching everything for help I can only do some of the problems half way and get stuck.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Sammyj View Post
    1) 2 ^3 sq rt 5 - 4 ^3 sq rt 40 + 3 ^3 sq rt 135
    If I am reading this correctly:
    2 \sqrt[3]{5} - 4 \sqrt[3]{40} + 3 \sqrt[3]{135}

    = 2 \sqrt[3]{5} - 4 \sqrt[3]{2^3 \cdot 5} + 3 \sqrt[3]{3^3 \cdot 5}

    = 2 \sqrt[3]{5} - 4 \cdot 2 \sqrt[3]{5} + 3 \cdot 3 \sqrt[3]{5}

    = 2 \sqrt[3]{5} - 8 \sqrt[3]{5} + 9 \sqrt[3]{5}

    = 3 \sqrt[3]{5}

    The key to simplifying \sqrt[n]{x} is to find factors of x that are
    powers of n. Such as the case of \sqrt[3]{135}: I knew to look for a factor of the form a^3, and by looking I found that 135 = 5 \cdot 27 = 5 \cdot 3^3. Then you can bring that number outside the radical.

    Try the other ones again. If you get stuck, post your solution and we'll see where things went sour.

    -Dan
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  3. #3
    Junior Member Sammyj's Avatar
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    Thanks a lot! This was very helpful
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