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anonymous
 one year ago
Can you show me how to do this?
A square picture frame occupies an area of 112 ft2. What is the length of each side of the picture in simplified radical form? Show your work.
anonymous
 one year ago
Can you show me how to do this? A square picture frame occupies an area of 112 ft2. What is the length of each side of the picture in simplified radical form? Show your work.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@SolomonZelman can you help me again? ^ ^;

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Since the picture frame is a square, and the area is 112 ft^2, then each side is \(\sqrt {112~ft^2} = \sqrt{112} ~ft\). Now we need to simplify \(\sqrt{112} \).

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1In order to simplify a root, you need to find the largest perfect square factor of the number whose root you are taking. What is the largest perfect square factor of 112?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1For example, if we were simplifying \(\sqrt{18} \), you could easily see that the largest perfect square factor of 18 is 9. 18 is an easy number to work with. 112 is not so easy. In order to figure it out, we find all the prime factors of 112.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Are you familiar with any method of finding the prime factors of a number?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mathstudent55 can you help me with a quick question please :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not fully aware No @mathstudent55

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Ok. I'll show you. Every whole number, 2 or larger is either a prime number or a composite number. A prime number is a number that can be divided evenly by only 2 different numbers, 1 and the number itself. A composite number can be divided evenly by more than 2 numbers. Every composite number is a product of prime numbers.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Here are the first several prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Other than 2, all other even numbers are composite.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1For example, the number 17 is prime. It is only divisible by 1 and 17. 18 is composite. It is divisible by 1, 2, 3, 6, 9, 18. In addition, since 18 is composite, it can be written as a product pf prime numbers. 18 = 2 * 3 * 3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay. Still not sure how to get 112.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we need to see which prime numbers have a product of 112. To find the prime factorization of 112, we start with 112 and divide it by 2, the smalles prime number. 112/2 = 56 We try to keep dividing by 2 as many times as is possible. 56/2 = 28 28/2 = 14 14/2 = 7 Since 7 is no longer divisible by 2, we move on to the next higher prime number that 7 is divisible by. Since 7 is prime, then 7 can be divided by 7. 7/7 = 1 You must always finish with 1. Now we see all the divisions we did to 1112 to end up with 1, and we have the prime factors of 112. 112 = 2 * 2 * 2 * 2 * 7

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Notice that 2 * 2 * 2 * 2 = 16, so 112 = 16 * 7, and 16 is a perfect square. \(\sqrt{112} = \sqrt{16 \times 7} = \sqrt{16}\times \sqrt{7} = 4 \sqrt {7}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright thanks @mathstudent55
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