2018-10-12 15:37:13 -04:00
---
title: Simplifying Square Roots
---
## Simplifying Square Roots
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.
2018-11-18 14:53:17 +11:00
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.
2018-10-12 15:37:13 -04:00
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.
2018-11-18 14:53:17 +11:00
So, it's a fact that:
2018-10-12 15:37:13 -04:00
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.
2018-11-18 14:53:17 +11:00
√ (x× y) = √ x × √ y
2018-10-12 15:37:13 -04:00
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.
2018-11-18 14:53:17 +11:00
and this fact allows us to understand that we can seperate the √ xy into two separate radicals, √ x and √ y.
2018-10-12 15:37:13 -04:00
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.
2018-11-18 14:53:17 +11:00
But first, we need to find a factor of 363, that would allow us to pull a perfect square from it.
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.
2018-10-12 15:37:13 -04:00
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.
2018-11-18 14:53:17 +11:00
Now, factors of 363 are: 1, 3, 11, 33, 121 and 363.
2018-10-12 15:37:13 -04:00
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.
2018-11-18 14:53:17 +11:00
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:
√ 363 = √ (121× 3) = √ 121 × √ 3
And we can take the square root of 121, where we can turn it into a whole number:
= 11 × √ 3
Hence, 11√ 3 is the square root number of 363.
## Simplifying Square roots in the Denominator:
Lets' say you have the expression:
< sup > 2< / sup > ⁄ < sub > √ 5< / sub >
And you wanted to simplify this by removing the radical from the denominator, well you can do this by multiplying this fraction by:
< sup > √ 5< / sup > ⁄ < sub > √ 5< / sub >
2018-10-12 15:37:13 -04:00
Which is equal to one, and you get:
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.
2018-11-18 14:53:17 +11:00
< sup > 2< / sup > ⁄ < sub > √ 5< / sub > × < sup > √ 5< / sup > ⁄ < sub > √ 5< / sub >
2018-10-12 15:37:13 -04:00
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.
2018-11-18 14:53:17 +11:00
= < sup > 2√ 5< / sup > ⁄ < sub > 5< / sub >
2018-10-12 15:37:13 -04:00
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.
2018-11-18 14:53:17 +11:00
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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