45 lines
1.7 KiB
Markdown
45 lines
1.7 KiB
Markdown
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---
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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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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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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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Now, factors of 363 are:
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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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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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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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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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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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#### 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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