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| 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.
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
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
Now, factors of 363 are: 1, 3, 11, 33, 121 and 363
If you look, you can see that 121 is among that list, 1213 is 363, and we can change the radical to show that: SQRT(363) = SQRT(1213) = SQRT(121)SQRT(3) And we can take the square root of 121, and make it a whole number: = 11Sqrt(3) And that's your radical.
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.