Question

find the cube root of -64/343 ​

Answer 1

Cube root of a number can be found by a very simple method which is the prime factorization method. Cube root is denoted by ‘∛ ‘ symbol. Example: ∛8 = ∛(2 × 2 × 2) = 2. Since, 8 is a perfect cube number, it is easy to find the cube root of a number.

Finding the cubic root of non-perfect cube number is a little complex process but can be mastered easily. To find the cube root of any number, we need to find a number which when multiplied three times by itself gives the original number.

Definition

The cube root of any number say ‘a’, is the number ‘b’, which satisfy the equation given below:

b3 = a

This can be represented as:

a = ∛b

How to Find Cube Root of a Number

Cube root is the inverse process of calculating the cube of a number. It is denoted by the symbol ‘∛’. Let us see some examples here now.

To find the cube root of a number 27, we want a number which when multiplied thrice with itself shall give 27. We can write,

27 = 3 × 3× 3 = 33

Taking cubic root on both the sides;

or ∛27 = ∛33

Therefore, the cube-root of 27 is 3.

note -  we will only consider the positive values cube roots of the natural numbers.

Answer:

The real root of:

−64−−−−√3

=−4

All roots:

2+3.46410162i

−4

2−3.46410162i

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