Cube Root смотреть онлайн

To cube a number, we multiply it by itself twice. For

example:

5 × 5 × 5 = (5^3) = 125

Finding the cube root of a number is the opposite operation of finding the cube of the number. For example:

∛125 = 5

The Cube Root of 125 means the number that should be multiplied by itself twice to get 125, and the answer is 5.

=====

Note:

The cube root of a positive number is a positive number, while the cube root of a negative number is a negative number. For example:

∛8 = 2

since

2 × 2 × 2 = (2^3) = 8

while

∛(−8) = (-2)

since

(-2) × (-2) × (-2) = ((−2)^3) = (-8)

-----

To find the cube root of a number:

1- Find the prime factors of the number.
2- Draw a bracket for every three similar prime factors.
3- Take one factor from each bracket.
4- Multiply the taken numbers together, and the result will represent the cube root of the original number.

Note that if we’re trying to find the cube root of a negative number, then we’ll find the prime factors of the number without the negative sign (-), and we’ll add the negative sign (-) to the final result obtained in step 4.

-----

Example 1:

Find the cube root of 216

Solution:

2 216
2 108
2 54
3 27
3 9
3 3
1

Therefore, ∛216= 2 × 3 = 6

-----

Note:

If we found that one or two prime factors were remained alone when we draw the brackets, then the cube root will equal the result of the multiplication of the numbers taken from each bracket multiplied by the cube roots of the remained factors.

Example 2:

Find the cube root of 24

Solution:

2 24
2 12
2 6
3 3
1

-----

Therefore, ∛24 = 2 × ∛3 = 2∛3

Example 3:

What’s the result of ∛(−1125)?

Solution:

First we’ll find the prime factors of the number without the negative sign (1125).

3 1125
3 375
5 125
5 25
5 5
1

-----

Therefore, ∛1125 = 5 × ∛3 × ∛3 = 5∛9

(Since ∛? × ∛? = ∛(? × ?))

Now we’ll add the negative sign (-) to the final result.

∛(−1125) = (-5∛9)

=====

Thank you for watching Math Mix YouTube channel.

Please Subscribe, Like, Comment, and Share.