To find cube root, make triple of equal factors. The opposite of cubing a number is called finding the cube root. A cube root is a number, that is multiplied by itself three times in order to create a cubic value. A cube root of a number x is a number, such that a^{3}= x. All real numbers (except zero) have exactly one real cube root.
Cube of 6 = 6³ =216
Cube root of 216 = 6
Examples
The symbol, \(\sqrt [3]{}\), means cube root, so \(\sqrt [3]{27}\) means "cube root of 27" and \(\sqrt[3]{64}\)means "Cube root of 64"
Thus \(\sqrt [3]{27}\) = \(\sqrt [3]{3^3}\) = 3 and \(\sqrt[3]{64}\) = \(\sqrt[3]{4^3}\) = 4
A natural number is known as a perfect cube or a cube number.
Cube root of a perfect cube can be found by factorization method.
Examples
Solution:
cube of 6
= 6^{3}
= 6×6×6
= 216
Solution:
Cube of 16
= 16^{3}
=16 ×16 ×16
= 4096
Solution:
cube root of 125
=\(\sqrt[3]{125}\)
=\(\sqrt[3]{5×5×5}\)
=\(\sqrt[3]{5^3}\)
= 5
5 | 125 |
5 | 25 |
5 |
Solution:
Cube of 20
= 20^{3}
= 20 × 20 × 20
= 8000
Soln: Cube of 35=(35)^{3}
=35×35×35
=42875
Solution:
Cube of 400
= 400^{3}
= 400×400×400
= 64000000
Solution:
3 | 81 |
3 | 27 |
3 | 9 |
3 |
81 = 3×3×3 =3^{3}
∴ The required number is 3.
Solution:
2 | 128 |
2 | 64 |
2 | 32 |
2 | 16 |
2 | 8 |
2 | 4 |
2 |
128 = 2^{3}×2^{3}×2
∴The required number is 2.
Solution:
3 | 135 |
3 | 45 |
3 | 15 |
5 |
135 = 3^{3}× 5
∴The required number is 5.
Solution:
Cube root of 1331
= \(\sqrt{1331}\)
= \(\sqrt[3]{11 ×11 ×11}\)
= 11
11 | 1331 |
11 | 121 |
11 |
Solution:
3 | 243 |
3 | 81 |
3 | 27 |
3 | 9 |
3 |
243 = 3^{3}× 3^{2}
∴The required number is 3.
Solution:
2 | 192 |
2 | 96 |
2 | 48 |
2 | 24 |
2 | 12 |
2 | 6 |
3 |
192 = 2^{3}×2^{3}×3
∴The required number is 3.
Solution:
5 | 625 |
5 | 125 |
5 | 25 |
5 |
325 = 5^{3}×5
∴The required number is 5.
Solution:
3 | 675 |
3 | 225 |
3 | 75 |
5 | 25 |
5 |
675 = 3^{3}×5^{2}
∴The required number is 5.
Find the cube of:
20
Find the cube of:
400
Find the cube root of:
125
Find the cube root of:
512
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.
243
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.
256
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.
72
Find the smallest numbers by which each of the following numbers must be divided to obtain a perfect cube.
81
Find the smallest numbers by which each of the following numbers must be divided to obtain a perfect cube.
128
Find the smallest numbers by which each of the following numbers must be divided to obtain a perfect cube.
135
Find the smallest numbers by which each of the following numbers must be divided to obtain a perfect cube.
192
Find the cube of:
(-70 )
Find the cube of:
0.06
Find the cube root of 5.832.
Find the cube root of:
10648
No discussion on this note yet. Be first to comment on this note