check whether a given natural number is a perfect square or not

Discussion in 'CBSE Class 8 Maths Help' started by sastry, Jan 28, 2011.

  1. sastry

    sastry New Member

    To check whether a given natural number is a perfect square or not, we follow the
    following steps:
    Step I Obtain the natural number.
    Stev II Write the number as a product of prime factors.
    Step -III Group the factors in pairs in such a way that both the factors in each pair are equal.
    Step IV See whether some factor is left over or not. If no factor is left over in grouping, then the given number is a perfect square. Otherwise, it is not a perfect square.
    Step V To obtain the number whose square is the given number take one factor from eaci. group and multiply them.

    Example 1 Is 225 a perfect square? if so, find the number whose square is 225.

    Sol : Resolving 225 into prime factors, we obtain
    225=3x3x5x5

    Grouping the factors in pairs in such a way that both the factors in each pair are equal, we have

    225 =(3x3) X (5x5)

    Clearly, 225 can be grouped into pairs of equal factors and no factor is
    left over. Hence, 225 is a perfect square.

    Again, 225=(3X5) X (3X5)
    =15 X 15 = 15^2
    So, 225 is the square of 15.

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