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14 February, 14:24

If root x + root y = root 45 and x and y are positive integers, then find the value of root x + y.

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  1. 14 February, 14:45
    0
    x = 5

    y = 20

    sqrt (x + y) = sqrt (25) = 5

    Step-by-step explanation:

    I think this is one of those things where you think you've been tricked and when you see the answer, you know you have.

    The root of 45 = root (5 * 3 * 3) = 3sqrt (5)

    Now you need to find some way of making x and y come to 3 sqrt (45)

    How about this? sqrt (5) + sqrt (20)

    square root 5 = 1 * sqrt (5)

    square root 20 = sqrt (2 * 2 * 5) = 2 sqrt (5)

    x = sqrt (5)

    y = 2*sqrt (5)

    1sqrt (5) + 2 sqrt (5) = 3 sqrt (5) which is the same thing as sqrt (45)

    It gets worse with part 2

    sqrt (x + y) = sqrt (5 + 20) = sqrt (25) = 5
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