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Math simplifying mixed radicals

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Please help me simplify these following mixed radicals:: and show me how you did it cause I need to learn :
I don't know how to type a square root sign so I just wrote square root:
2 square root 48
3 square root 81
6 square root 12
3 square root 32
2 square root 18
5 square root 48
3 square root 54
Thanks :)

  • Math simplifying mixed radicals - ,

    Hi! Just to clarify, are those numbers on the left (the 2, 3, 6, 3, etc.) are multiplied with the squareroot terms or are written as small number which is therefore part of the radical sign?

  • Math simplifying mixed radicals - ,

    They are multiplied

  • Math simplifying mixed radicals - ,

    To do this, you have to factor the radicand (or the number inside the radical sign) and look for perfect squares. For instance,
    2 * √(48)
    2 * √(16*3)
    2 * √(4*4*3)
    Express the repeating factors using exponents, so it's easier to see. Since four is multiplied by itself twice,
    2 * √((4^2) * 3)
    The 4^2 is a perfect square, it's squareroot is equal to 4. Therefore you have,
    2 * 4 √(3)
    = 8 * √(3)

    #2.
    3 * √(81)
    3 * √(9*9)
    3 * √(9^2)
    3 * 9
    = 27

    #3.
    6 * √(12)
    6 * √(2*2*3)
    6 * √((2^2) * 3)
    6 * 2 * √(3)
    = 12 * √(3)

    #4.
    3 * √(32)
    3 * √(8*4)
    3 * √(2*4*4)
    3 * √((4^2) * 2)
    3 * 4 * √(2)
    = 12 * √(2)

    Now, try solving the rest.
    Hope this helps~ :3

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