Cube Root

A number m is the cube root of a number n
if n = m³.
In other words, the cube-root of a number n is that number whose cube gives n.
The cube-root of a number is denoted by ∛n. ∛n is also called a radical, n is called the radicand and 3 is called the index of the radical.

8 = 2³ ∴ ∛8 = 2 ;

27 = 3³ ∴ ∛27 = 3 ;

343 = 7³ ∴ ∛343 = 7 ;

-125 = (-5)³ ∴ ∛(-125) = -5 ;

(64/125) = (4/5)³ ∴ ∛(64/125) = 4/5 ;

(216) = 6³ ∴ ∛216 = 6 ;

(1000) = 10³ ∴ ∛1000 = 10 ;

Cube	Cube-Root (∛ )	Cube	Cube-Root (∛ )
1	1	11	1331
8	2	1728	12
27	3	2197	13
64	4	2744	14
125	5	3375	15
216	6	6656	16
343	7	4913	17
512	8	5832	18
729	9	6859	19
1000	10	8000	20

Remark : The symbol ∛ for the cube-root is very much similar to the symbol of square root. The only difference is that whereas in the case of square root, we use the symbol '√' for the cube-root we use the same symbol √ but a 3 which indicates that we are taking cube-root.
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Practice
1) If (1331) = 11³ then ∛1331 = ______ ;

2) If (125/1000) = 5³/10³ then ∛(125/1000) = _________

3) If (6859) = 18³/10³ then ∛6859 = _________

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Cube and Cube-Roots

• Cube of Numbers
• Perfect- Cube
• Properties of Cube
• Cube -Column method
• Cube - Negative numbers
• Cube- Rational numbers
• Cube Root
• Finding cube-root by Prime Factorization
• Cube-root of Rational numbers
• Estimating cube-root

From Cube and Cuberoot to Exponents

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