Cube Root

A number m is the cube root of a number n
if n = m
3 .
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) = 11
3 then ∛1331 = ______ ;

2) If (125/1000) = 5
3 /10 3 then ∛(125/1000) = _________

3) If (6859) = 18
3 /10 3 then ∛6859 = _________




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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