5 is the <em>smallest</em> number by which 35280 must be multiplied so that the product will be a <em>perfect</em> square.
<h3>What number must be an integer multiplied by to find a perfect square? </h3>
A number is a <em>perfect</em> square if the following property is satisfied:
a = b², where is a <em>natural</em> number.
Please notice that b can be either a <em>prime</em> number or a product of <em>prime</em> numbers.
Initially, we proceed to factorize 35280 by factorial decomposition, that is, as a product of <em>prime</em> 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 <em>smallest</em> number by which 35280 must be multiplied so that the product will be a <em>perfect</em> square.
To learn more on prime numbers: brainly.com/question/9315685
#SPJ1
