The value of the cube root of 64 is 4. It is the real solution of the equation x3 = 64. The cube root of 64 is expressed as ∛64 in radical form and as (64)⅓ or (64)0.33 in the exponent form. As the cube root of 64 is a whole number, 64 is a perfect cube.

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**Cube root of 64:**4

**Cube root of 64 in exponential form:**(64)⅓

**Cube root of 64 in radical form:**∛64

1. | What is the Cube Root of 64? |

2. | How to Calculate the Cube Root of 64? |

3. | Is the Cube Root of 64 Irrational? |

4. | FAQs on Cube Root of 64 |

The cube root of 64 is the number which when multiplied by itself three times gives the product as 64. Since 64 can be expressed as 2 × 2 × 2 × 2 × 2 × 2. Therefore, the cube root of 64 = ∛(2 × 2 × 2 × 2 × 2 × 2) = 4.

In this section, we will learn how to calculate the cube root of 64 step-wise.

### Cube Root of 64 by Prime Factorization

**Step 1**: Determine the prime factorization of 64 i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2

**Step 2**: Group the prime factors of 64 in groups of three each. 64 = (2 × 2 × 2) × (2 × 2 × 2) = 23 × 2 3

**Step 4**: Take the cube root on both sides of the equation.

Therefore, the cube root of 64 by prime factorization is (2 × 2 × 2 × 2 × 2 × 2)1/3 = 4.

No, because ∛64 = ∛(2 × 2 × 2 × 2 × 2 × 2) can be expressed in the form of p/q i.e. 4/1. Therefore, the value of the cube root of 64 is an integer (rational).

**☛ Also Check:**

**Example 3: What is the value of ∛64 ÷ ∛(-64)?**

**Solution: **

The cube root of -64 is equal to the negative of the cube root of 64.⇒ ∛-64 = -∛64Therefore,⇒ ∛64/∛(-64) = ∛64/(-∛64) = -1

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## FAQs on Cube Root of 64

### What is the Value of the Cube Root of 64?

We can express 64 as 2 × 2 × 2 × 2 × 2 × 2 i.e. ∛64 = ∛(2 × 2 × 2 × 2 × 2 × 2) = 4. Therefore, the value of the cube root of 64 is 4.

### How to Simplify the Cube Root of 64/125?

We know that the cube root of 64 is 4 and the cube root of 125 is 5. Therefore, ∛(64/125) = (∛64)/(∛125) = 4/5 = 0.8.

### Is 64 a Perfect Cube?

The number 64 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 2. Combining the prime factors in groups of 3 gives 4. So, the cube root of 64 = ∛(2 × 2 × 2 × 2 × 2 × 2) = 4 (perfect cube).

### If the Cube Root of 64 is 4, Find the Value of ∛0.064.

Let us represent ∛0.064 in p/q form i.e. ∛(64/1000) = 4/10 = 0.4. Hence, the value of ∛0.064 = 0.4.

### Why is the Value of the Cube Root of 64 Rational?

The value of the cube root of 64 can be expressed in the form of p/q i.e. = 4/1, where q ≠ 0. Therefore, the ∛64 is rational.

### What is the Value of Cube Root of -64?

We know that the cube root of negative numbers is negative.

Write -64 as a product of its prime factors: -64= -(2 × 2 × 2 × 2 × 2 × 2)Club the factors into groups of three each: -64= -23 × 23 = -43Take the cube root on both sides of the equation: 3**√**-64 = 3

**√**-43= -4

Hence, the cube root of -64 is -4.

### Find if Cube Root of 64 Minus Cube Root of 8 is a Rational Number?

The value of cube root of 64 and 8 is 4 and 2 respectively i.e. 3**√**64 - 3**√**8 = 4 - 2 = 2. Hence, the difference between the cube root of 64 and the cube root of 8 is a rational number.

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### What is the Cube of the Cube Root of 64?

The cube of the cube root of 64 is the number 64 itself i.e. (∛64)3 = (641/3)3 = 64.