Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Find the smallest number by which 35280 must be multiplied so that the product is a perfect square.

Sagot :

xero099

5 is the smallest number by which 35280 must be multiplied so that the product will be a perfect square.

What number must be an integer multiplied by to find 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

#SPJ1

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.