Math simplifying mixed radicals

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 and the numbers infront of the square root are supposed to be multiplied.
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 :)

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asked by Miley
  1. 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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    posted by Jai
  2. the square root of 20 minus the sqare root of 5 plus the square root of 45

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    posted by john

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