Cube Root
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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 = 2^{3} ∴ ∛8 = 2 ;
27 = 3^{3} ∴ ∛27 = 3 ;
343 = 7^{3} ∴ ∛343 = 7 ;
-125 = (-5)^{3} ∴ ∛(-125) = -5 ;
(64/125) = (4/5)^{3} ∴ ∛(64/125) = 4/5 ;
(216) = 6^{3} ∴ ∛216 = 6 ;
(1000) = 10^{3} ∴ ∛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.
_______________________________________________________________
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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