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Perfect SquaresProcedure to check whether a given natural number is a perfect squares or not.Step I : Obtain the natural number. Step 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 the grouping, then the given number is a perfect square. Otherwise, it is not a perfectsquare. Step V: To obtain the number whose square is the given number taken over one factor from each group and multiply them. Examples on perfectsquare 1) Is 225 a perfectsquare? If so, find the number whose square is 225. Solution : Resolving 225 into prime factors, we obtain 225 = 3 x 3 x 5 x 5 Grouping the factors in pairs in such a way that both the factors in each pair are equal, we have 225 = ( 3 x 3 ) x ( 5 x 5 ) Clearly, 225 can be grouped into pairs of equal factors and no factor is left over. Hence, 225 is a perfectsquare. Again, 225 = (3 x 5) x (3 x 5) = 15 x 15 = 15 ^{2} So, 225 is the square of 15. ________________________________________________________________ 2) Is 150 a perfectsquare? If so,find the number whose square is 150. Solution : Resolving 150 into prime factors, we obtain 150 = 2 x 3 x 5 x 5 Grouping the factors in pairs in such a way that both the factors in each pair are equal, we have 225 = 2 x 3 x ( 5 x 5 ) Clearly, 150 can be grouped into pairs of equal factors.2 and 3 factors are left over. Hence, 150 is not a perfectsquare. _______________________________________________________________ Q.1 Check whether the following numbers are perfect squares or not, give reason. 1) 250 2) 289 3) 1024 4) 1156 5) 1000 Q.2 The following numbers are perfectsquares,find whose perfectsquares are those. 1) 2 x 3 x 3 x 2 x 5 x 5 2) 7 x 7 x 2 x 11 x 2 x 11 3) 2 x 3 x 3 x 2 x 7 x 7 Squares and Square roots • Introduction of Squares and Square Roots • Perfect Squares or not • Properties of Square Numbers • Short cut method to find squares • Introduction of Square Roots • Properties of Square Roots • Square root by Prime factorization method • Square root by long division method • Square root of rational numbers • Square root of Decimals • Square root by estimation method Home Page
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