Question

By what number should each of the following numbers e multiplied to get a perfect square in ea h case ? Also find the number whose square in the new number .
8820

Answer 1

Answer:

We are going to find out prime factors of 8820

8820=2×4410

=2×2×2205

=2×2×3×735

=2×2×3×3×245

=2×2×3×3×5×49

=2×2×3×3×5×7×7

By grouping the prime factors for 23805

=(2×2)×(3×3)×(7×7)×5

By observation, prime factor 5 is left out.

So, multiply by 5 we get,

8820×5 =(2×2)×(3×3)×(7×7)×(5×5)

=(2×3×5×7)×(2×3×5×7)

=210×210

=(210) 2

44100=(210) 2

√44100 =210

Hence, the number by which 8820 must be multiplied so that the product is perfect square is 5.

So, the sum will be 210+5=215