How to Simplify Roots

When you work with roots in an equation, you often need to simplify them. There are two methods: the quick, sort of intuitive method, and a slightly longer method. The quick method of simplification works only with some roots, like

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The quick method works for the square root of 300 because it’s easy to see a large perfect square, 100, that goes into 300. Because 300 equals 100 times 3, the 100 comes out as its square root, 10, leaving the 3 inside the square root. The answer is thus

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It’s not as easy to find a large perfect square that goes into 504, so you’ve got to use the longer method to solve it.

  1. Break 504 down into a product of all of its prime factors.

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  2. Circle or identify each pair of numbers.

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  3. For each pair you identify, take one number out.

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  4. Simplify.

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The last thing about roots is that by convention, you don’t leave a root in the denominator of a fraction — it’s a silly, anachronistic convention, but it’s still being taught, so here it is.

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