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horrorfan [7]
2 years ago
14

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

Mathematics
1 answer:
nlexa [21]2 years ago
5 0

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

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3 years ago
If a = 38 ft, b = 15 ft, c = 19 ft, and d = 19 ft, what is the area of the living room and hallway together?
Anvisha [2.4K]

Answer:

The area of the living room and hallway together = 437ft²

Question:

The complete question related to the one above found at 'Geometry in class' is stated below:

Abbey is getting new carpet in her living room and hallway.

The following diagram shows the two together.

If = 38 ft, b = 15 ft, c = 19 ft, and d = 19 ft, what is the area of the living room and hallway together?

Find attached the diagram of the question.

Step-by-step explanation:

To determine the area of the living room and hallway together, we would break the diagram into two rectangles.

Calculate the area of each and sum the two outcomes together.

Find attached the diagrams of the solution.

Given: a = 38 ft, b = 15 ft, c = 19 ft, and d = 19 ft,

Area of rectangle = length × breadth

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= 38 × (19-15) = 38× 4

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The area of the living room and hallway together = Area of rectangle 1 + Area of rectangle 2

= 152ft² + 285ft²

The area of the living room and hallway together = 437ft²

5 0
3 years ago
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