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cube root∗
Daume†
2013-03-21 12:46:24
√
The cube root of a real number x, written as 3 x, is the real number y such
√
√
√ √
3
that y 3 = x. Equivalently, 3 x = x. Or, 3 x 3 x 3 x = x. √The cube root
1
notation is actually an alternative to exponentiation. That is, 3 x = x 3 .
Properties:
• The
cube
operation of an exponentiation has the following property:
√
√ root
n
3
xn = 3 x .
• The cube root operation is distributive for multiplication and division,
but
q
√
√ √
3 x
√
not for addition and subtraction. That is, 3 xy = 3 x 3 y, and 3 xy = √
3 y.
• However, in general, the cube root operation
is not distributive for
√
√ addition
√
√
√
√
and substraction. That is, 3 x + y 6= 3 x + 3 y and 3 x − y 6= 3 x − 3 y.
• The cube root is a special case of the general nth root.
• The cube root is a continuous mapping from R → R.
• The cube root function from R → R defined as f (x) =
function.
√
3
x is an odd
Examples:
√
1. 3 −8 = −2 because (−2)3 = (−2) × (−2) × (−2) = −8.
√
2. 3 x3 + 3x2 + 3x + 1 = x + 1 because (x + 1)3 = (x + 1)(x + 1)(x + 1) =
(x2 + 2x + 1)(x + 1) = x3 + 3x2 + 3x + 1.
p
3. 3 x3 y 3 = xy because (xy)3 = xy × xy × xy = x3 y 3 .
q
3
8
8
4. 3 125
= 52 because ( 25 )3 = 253 = 125
.
∗ hCubeRooti
created: h2013-03-21i by: hDaumei version: h30748i Privacy setting: h1i
hDefinitioni h11-00i
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