Root question, surds?

8√8 can be turned into m√2, where m is a positive integer.

Find m, and explain how you found it

4 Answers

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  • Puggy
    Lv 7
    1 decade ago
    Favorite Answer

    In order to reduce radicals (square roots), you have to decompose what's inside the square root.

    sqrt(8) is the same as sqrt(4 * 2).

    The square root of a product is the product of its square roots.

    so sqrt(4 * 2) = sqrt(4) * sqrt(2)

    We know what the square root of 4 is. It's 2.

    sqrt(4)sqrt(2) = 2 sqrt(2).

    In the above case, it's the exact same

    8sqrt(8) = m sqrt(2)

    8 sqrt(4*2) = m sqrt(2)

    8 sqrt(4)sqrt(2) = m sqrt(2)

    8*2*sqrt(2) = m sqrt(2)

    16 sqrt(2) = m sqrt(2)

    Therefore, m = 16

  • Luiz S
    Lv 7
    1 decade ago

    8√8 = m√2

    8√(4*2) = m√2

    8√4√2 = m√2

    8*2√2 = m√2

    16√2 = m√2

    m = 16

  • 1 decade ago

    You find it by rewriting √8 as √(4 x √2, and replacing √4 with 2

    So you have 8 x 2 √2 which is 16 √2

    So m = 16

  • 1 decade ago

    Turn it into an equation:

    8*sqrt(8) = m*sqrt(2)

    divide both sides by sqrt(2):

    8* sqrt(8)/sqrt(2) = m

    m = 8 * sqrt(8/2)

    m = 8 * sqrt (4)

    m = 8 * 2

    m=16

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