The worth of the cube source of 64 is 4. The is the genuine solution of the equation x3 = 64. The cube source of 64 is expressed as ∛64 in radical kind and as (64)⅓ or (64)0.33 in the exponent form. As the cube source of 64 is a totality number, 64 is a perfect cube.

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Cube source of 64: 4Cube source of 64 in exponential form: (64)⅓Cube root of 64 in radical form: ∛64

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1.What is the Cube source of 64?
2.How to calculation the Cube source of 64?
3.Is the Cube root of 64 Irrational?
4.FAQs ~ above Cube root of 64

The cube root of 64 is the number which as soon as multiplied through itself 3 times offers the product as 64. Due to the fact that 64 deserve to 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 exactly how to calculate the cube root of 64 step-wise.

Cube source of 64 by element Factorization

Step 1: recognize the element factorization of 64 i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2Step 2: group the prime components of 64 in teams of 3 each. 64 = (2 × 2 × 2) × (2 × 2 × 2) = 23 × 2 3Step 4: take the cube source on both sides of the equation.

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


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

☛ additionally Check:


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

Solution:

The cube root of -64 is same to the an adverse of the cube source 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 together 2 × 2 × 2 × 2 × 2 × 2 i.e. ∛64 = ∛(2 × 2 × 2 × 2 × 2 × 2) = 4. Therefore, the worth 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 also the cube source of 125 is 5. Therefore, ∛(64/125) = (∛64)/(∛125) = 4/5 = 0.8.

Is 64 a Perfect Cube?

The number 64 on prime factorization provides 2 × 2 × 2 × 2 × 2 × 2. Combine the prime components in teams of 3 provides 4. So, the cube source of 64 = ∛(2 × 2 × 2 × 2 × 2 × 2) = 4 (perfect cube).

If the Cube source of 64 is 4, discover the value of ∛0.064.

Let us stand for ∛0.064 in p/q type i.e. ∛(64/1000) = 4/10 = 0.4. Hence, the worth of ∛0.064 = 0.4.

Why is the value of the Cube source of 64 Rational?

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

What is the worth of Cube source of -64?

We understand that the cube source of an adverse numbers is negative.

Write -64 together a product of its prime factors: -64= -(2 × 2 × 2 × 2 × 2 × 2)Club the determinants into groups of three each: -64= -23 × 23 = -43Take the cube source on both political parties of the equation: 3-64 = 3-43= -4

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

Find if Cube root of 64 Minus Cube source of 8 is a rational Number?

The worth of cube root of 64 and 8 is 4 and also 2 dong i.e. 364 - 38 = 4 - 2 = 2. Hence, the difference in between the cube source of 64 and also the cube source of 8 is a reasonable number.

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What is the Cube that the Cube root of 64?

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