Equation symbol changes and formatting changes (#22049)
* Equation symbol changes and formatting changes -Initially, SQRT(value) does not actually create a square root symbol, so I decided to use replace SQRT( ) with √ next to the number, which has successfully created the square root symbol to the left of the number. -Given that the information of the article was unorganized through jumbled information, I decided to use the paragraph tag, <p>, to make the article have an organized structure. -I also used the biggest headline tag, <h1>, to outline the topics of square roots -Given that '-----' was not an effective method of creating fractions, I decided to use the fraction slash tag, "⁄", the superscript element, <sup>, and the subscript element, <sub>, in order to create suitable fractions * Removing unnecessary coding and editing content -I just double checked this content, and realized that there were a couple of mistakes such as an extra heading, putting a square root as sqrt(3) instead of √3, and adding unnecessary paragraph tags instead of extra spaces.
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Christopher McCormack
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@ -3,42 +3,45 @@ title: Simplifying Square Roots
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---
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## Simplifying Square Roots
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Simplied Radical form:
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Let's say you have the radical SQRT(363), and you need to simplify it into both a nicer looking number and a number that you can use in specific calculations, to do this by trying to find perfect squares within the radical.
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Let's say you have the radical √363, and you need to simplify it into a both, simplest number, and a number that you can use in specific calculations, where we can do this by trying to find perfect squares within the radical.
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So, it's a fact that SQRT(x*y) = SQRT(x) + SQRT(y)
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and this fact allows us to seperate the SQRT(243) into pieces
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So, it's a fact that:
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but first, we need to find a factor of 363, tha would allow us to pull a perfect square from it.
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Perfect squares include 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144... because each of them has a sqare root that is a whole number
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√(x×y) = √x × √y
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Now, factors of 363 are:
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1, 3, 11, 33, 121 and 363
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and this fact allows us to understand that we can seperate the √xy into two separate radicals, √x and √y.
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If you look, you can see that 121 is among that list, 121*3 is 363, and we can change the radical to show that:
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SQRT(363) = SQRT(121*3)
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= SQRT(121)*SQRT(3)
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And we can take the square root of 121, and make it a whole number:
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= 11*Sqrt(3)
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And that's your radical.
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But first, we need to find a factor of 363, that would allow us to pull a perfect square from it.
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Perfect square numbers include: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 etc. ,as each of them can become a whole number if these numbers were square rooted.
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Now, factors of 363 are: 1, 3, 11, 33, 121 and 363.
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If you look, you can see that 121 is among that list, 121×3 is 363, and we can change the radical to show that:
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Simplifying Square roots in the denominator:
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√363 = √(121×3) = √121 × √3
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And we can take the square root of 121, where we can turn it into a whole number:
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= 11 × √3
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Hence, 11√3 is the square root number of 363.
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## Simplifying Square roots in the Denominator:
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Lets' say you have the expression:
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2
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-------
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SQRT(5)
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<sup>2</sup>⁄<sub>√5</sub>
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And you wanted to simplify this by removing the radical from the denominator, well you can do this by multiplying this fraction by:
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SQRT(5)
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-------
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SQRT(5)
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<sup>√5</sup>⁄<sub>√5</sub>
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Which is equal to one, and you get:
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2 SQRT(5) 2 x SQRT(5)
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------- x ------- = ----------- because a square root multiplied by itself is the number in the square, the denominator is now a
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SQRT(5) SQRT(5) 5 whole number, not a radical. The radical still exists in the top, but this is fine in most cases.
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<sup>2</sup>⁄<sub>√5</sub> × <sup>√5</sup>⁄<sub>√5</sub>
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= <sup>2√5</sup>⁄<sub>5</sub>
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because a square root multiplied by itself is the number in the square, the denominator is now a whole number, not a radical anymore. The radical still exists in the top, but this is fine in most cases, as the value itself is still exact.
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#### More Information:
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<!-- Please add any articles you think might be helpful to read before writing the article -->
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