5 is the smallest number by which 35280 must be multiplied so that the product will be a perfect square.
A number is a perfect square if the following property is satisfied:
a = b², where is a natural number.
Please notice that b can be either a prime number or a product of prime numbers.
Initially, we proceed to factorize 35280 by factorial decomposition, that is, as a product of prime numbers:
35280 = 2⁴ × 3² × 5 × 7²
35280 = (2²)² × 3² × 5 × 7²
35280 = 4² × 3² × 5 × 7²
Then, we must add a 5 to find a product that is a perfect square:
4² × 3² × 5² × 7² = 176400
5 is the smallest number by which 35280 must be multiplied so that the product will be a perfect square.
To learn more on prime numbers: https://brainly.com/question/9315685
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