the number 87120 is not a perfect square. find the smallest number by which it should be multiplied to make it a perfect square. alsofind the number which should be added to make it a perfect square.

87120  

223+45

hey robin this is easy. u can write 87120 in terms of its prime factors as 2⁴*5¹*3²*11²

now 3 and 11 have power 2.

2 has power 4 (which is a multiple of 2)

but 5 has power 1. so if we multiple by 5 it will also have a power 2 and the final number will become a perfect square.

so we need to multiply 87120 by 5 = 435600

the number 87120 is not a perfect square.

  87120 = (2x2)(2x2)(3x3)(11x11)x5

hence the smallest number by which 87120 should be multiplied and added to get a perfect square is 5 

87120 x 5 = 2 x 2 x 2 x 2 x 3 x 3 x 11 x 11 x 5 x 5

sorry it should not be added to 5 it would only be multiplied by 5. d correct answer is

first we'll find the square of the 87120. so the quotient of this is 295 and remainder is 95

thus it is evident that 295² < 87120 < 296²

296² = 87616

295²=87025

87616-87025=591 thus 87120 should be added to 591 to get a perfect square 

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