
HigherIndex Roots: Basic Operations (page 6 of 7) Sections: Square roots, More simplification / Multiplication, Adding (and subtracting) square roots, Conjugates / Dividing by square roots, Rationalizing denominators, HigherIndex Roots, A special case of rationalizing / Radicals & exponents / Radicals & domains Operations with cube roots, fourth roots, and other higherindex roots work similarly to square roots. Simplifying HigherIndex Terms
Just as I can pull from a square (or second) root anything that I have two copies of, so also I can pull from a fourth root anything I've got four of: If you have a cube root, you can take out any factor that occurs in threes; in a fourth root, take out any factor that occurs in fours; in a fifth root, take out any factor that occurs in fives; etc.
Multiplying HigherIndex Roots
Adding HigherIndex Roots
Dividing HigherIndex Roots
I can't simplify this expression properly, because I can't simplify the radical in the denominator down to whole numbers: To rationalize a denominator containing a square root, I needed two copies of whatever factors were inside the radical. For a cube root, I'll need three copies. So that's what I'll multiply onto this fraction:
Since 72 = 8 × 9 = 2 × 2 × 2 × 3 ×3, I won't have enough of any of the denominator's factors to get rid of the radical. To simplify a fourth root, I would need four copies of each factor. For this denominator's radical, I'll need two more 3s and one more 2:
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