Question

find the smallest number by which each of the given numbers should be multiplied so that the product is a perfect square.
3675
1323
2205
also please explain this. how to do​

Answer 1

Answer:

Hence the sum will be 105+3=108

Step-by-step explanation:

$qustions$

By what number should 3675 be multiplied to get a perfect square in each case? Also, find the number whose square in the new number.

Find the sum of those 2 numbers.

$answer$

We are going to find out prime factors of 3675

3675=3×1225

=3×5×245

=3×5×5×49

=3×5×5×7×7

By grouping the prime factors for 3675

=(5×5)×(7×7)×3

By observation, prime factor 3 is left out.

So, multiply by 3 we get,

3675×3 =(5×5)×(7×7)×(3×3)

=(5×7×3)×(5×7×3)

=105×105

=(105)

2

11025=(105)

2

11025

=105

Hence, the number by which 3675 must be multiplied so that the product is perfect square is 3.

Hence the sum will be 105+3=108