diff --git a/guide/english/mathematics/simplifying-square-roots/index.md b/guide/english/mathematics/simplifying-square-roots/index.md index 43f3c0cca2..3706ac4055 100644 --- a/guide/english/mathematics/simplifying-square-roots/index.md +++ b/guide/english/mathematics/simplifying-square-roots/index.md @@ -3,42 +3,45 @@ title: Simplifying Square Roots --- ## Simplifying Square Roots -Simplied Radical form: -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. +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. -So, it's a fact that SQRT(x*y) = SQRT(x) + SQRT(y) -and this fact allows us to seperate the SQRT(243) into pieces +So, it's a fact that: -but first, we need to find a factor of 363, tha would allow us to pull a perfect square from it. -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 +√(x×y) = √x × √y -Now, factors of 363 are: -1, 3, 11, 33, 121 and 363 +and this fact allows us to understand that we can seperate the √xy into two separate radicals, √x and √y. -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: -SQRT(363) = SQRT(121*3) - = SQRT(121)*SQRT(3) -And we can take the square root of 121, and make it a whole number: - = 11*Sqrt(3) -And that's your radical. +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. +Now, factors of 363 are: 1, 3, 11, 33, 121 and 363. +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: + +2√5 + +And you wanted to simplify this by removing the radical from the denominator, well you can do this by multiplying this fraction by: + +√5√5 -Simplifying Square roots in the denominator: -Lets' say you have the expression: - 2 -------- -SQRT(5) -And you wanted to simplify this by removing the radical from the denominator, well you can do this by multiplying this fraction by: -SQRT(5) -------- -SQRT(5) Which is equal to one, and you get: - 2 SQRT(5) 2 x SQRT(5) -------- x ------- = ----------- because a square root multiplied by itself is the number in the square, the denominator is now a -SQRT(5) SQRT(5) 5 whole number, not a radical. The radical still exists in the top, but this is fine in most cases. + +2√5 × √5√5 + += 2√55 + +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. #### More Information: - -