How to Factor Rolled Functions
How to Factor Diced Roots
To simplify a diced root, you need to take it into account. Factoring a cube root is like any other number. The difference is that you have to find numbers that are cube-shaped to remove them from the radical sign. Fortunately, there aren't many numbers that can be rolled without getting very large. That means that in general, when you have to consider a cube root in school, you are dealing with small factors.
Calculate factor 2s. If the cube root is even, then the number 2 must be factored out until the number is odd. For the diced For example, we get the root of 40: 40 = 2 × 20 = 2 × 2 × 10 = 2 × 2 × 2 × 5
Calculate the factor 3s. You can tell if a number has the number 3 as a factor by adding up the whole numbers and seeing if they add up to a power of 3. For example, 15 is divisible by 3 because 1 + 5 = 6 3. As in step 1, factor out 3 until you can no longer do the math: 54 = 2 x 27 = 2 x 3 x 9 = 2 x 3 x 3 x 3
Factor the 5s off. You can say a number has 5 as a factor because it ends in 0 or 5.
Factor from the 7s. Unfortunately there is no clear pattern for 7s. You'll either need to memorize your 7 multiplication table or divide the number experimentally to see if it divides evenly.
After fully accounting for the rolled root, move any number that goes three times into the left side of the radical. For example: ³? 8 = ³? 2 x 2 x 2 = 2
Multiply numbers that you cannot remove from the radical sign to get the final shape of the rolled root: ³? 120 = ³? 2 x 60 = ³? 2 x 2 x 30 = ³? 2 x 2 x 2 x 15 = 2 x 2 x 2 x 3 x 5 = 2³ - 3 x 5 = 2³? 15th
Occasionally you get diced root with 11, 13, 17 or other high prime numbers. There is no easy way to rule out high prime numbers. All you have to do is guess and check.
It's easy to confuse cube roots and square roots. Remember, in square roots you are squaring numbers that are squared under the radical sign, but in diced roots you are working out numbers that are diced.
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