Question

find the smallest number by which of the given number must be multiplied so that the product is a perfect square (a)512 (b)700 (c) 1323 (d) 35280
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Answer 1

First find the prime factors of 1323

1323=3×441

=3×3×147

=3×3×3×49

=3×3×3×7×7

3×3×3×7×7 are they prime factors of 1323

now form pairs of two same numbers which number remains only one is your answer

means here you have to multiply 1323 by 3

now similarly find prime factors of 35280

35280=2×17640

=2×2×8820

=2×2×2×4410

=2×2×2×2×2205

=2×2×2×2×3×735

=2×2×2×2×3×3×245

=2×2×2×2×3×3×5×49

=2×2×2×2×3×3×5×7×7

here 5 left alone so your answer is 5

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