Question

By what least number should 3675 be multiplied to get a perfect square number? Also, find the number whose square is the new number​

Answer 1

Answer:

$3657 = 3 \times 1225 \\ = 3 \times 5 \times 245 \\ = 3 \times 5 \times 5 \times 49 \\ = 3 \times 5 \times 5 \times 7 \times 7$

by grouping the prime factors for 3675

$= (5 \times 5) \times ( 7 \times 7) \times 3$

by observation prime factor 3 is left out.

so multiply by 3 we get,

$3675 \times 3 = 5 \times 5 \times 7 \times 7 \times 3 \times 3$

$= 5 \times 7 \times 3 \times 5 \times 3 \times 7$

$= 105 \times 105$

$= (105) ^{2}$

$= 11025 = (105) ^{2}$

$\sqrt{11025 = 105}$

hence the sum will be 105+3=108