What is cube root of 64

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In math, the cube root of a number like 64 is a number that, when multiplied by itself two times, is equal to 64.

We would show this in mathematical form with the cube root symbol, which is similar to the radical symbol (√) used in a square root, but which also has the number 3 above the symbol (this number is called the index):

So, the √ is called the radical symbol, the little 3 above it is the index (which means multiply by itself two more times), and the number, 64, is called the radicand.

To explain the cube root a little more, the cube root of the number 64 is a number (which we call n) that when multiplied by itself twice is equal to 64:

∛64 is the same as 64⅓ and so if you are solving a problem in a spreadsheet like Excel, Numbers, or Google Sheets, you can use =64^(1/3) to calculate the cube root.

For the purposes of this article, we'll use a scientific calculator to work out the cubic root by typing the number 64 and pressing the [∛x] button, to give the following answer:

Is 64 a Perfect Cube?

When the cube root of a given number is a whole number, this is called a perfect cube. Perfect cubes are important for many mathematical functions and are used in everything from carpentry through to more advanced topics like physics and astronomy.

If we look at the number 64, we know that the cube root is 4, and since this is a whole number, we also know that 64 is a perfect cube.

If you want to learn more about perfect cube numbers we have a list of perfect cubes which covers the first 500 perfect cube numbers.

Is the Cube Root of 64 a Rational or Irrational Number?

Another common question you might find when working with the roots of a number like 64 is whether the given number is rational or irrational. Rational numbers can be written as a fraction and irrational numbers can't.

The quickest way to check if a number is rational or irrational is to determine if it is a perfect cube. If it is, then it's a rational number, but if it is not a perfect cube then it is an irrational number.

We already know that 64 is a rational number then, because we know it is a perfect cube.

Rounding the Cube Root of 64

Sometimes when you work with the cube root of 64 you might need to round the answer down to a specific number of decimal places:

10th: ∛64 = 4.0

100th: ∛64 = 4.00

1000th: ∛64 = 4.000

Simplifying the Cube Root of 64

It is possible to simplify the cube root of 64 if the radicand can be made smaller. When that is possible, it is called the cube root of 64 in its simplest radical form.

In this example, the cube root of 64 in its simplest form is:

Practice Cube Roots Using Examples

If you want to continue learning about cubic roots, take a look at the random calculations in the sidebar to the right of this blog post.

We have listed a selection of completely random numbers that you can click through and follow the information on calculating the cubic root of that number to help you understand number roots.

Calculate Cube Square Root Problem

Use this calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x positive a will be positive, if x is negative a will be negative. Cube roots is a specialized form of our common radicals calculator.

Example Cube Roots:

• The 3rd root of 64, or 64 radical 3, or the cube root of 64 is written as \( \sqrt[3]{64} = 4 \).
• The 3rd root of -64, or -64 radical 3, or the cube root of -64 is written as \( \sqrt[3]{-64} = -4 \).
• The cube root of 8 is written as \( \sqrt[3]{8} = 2 \).
• The cube root of 10 is written as \( \sqrt[3]{10} = 2.154435 \).

The cube root of x is the same as x raised to the 1/3 power. Written as \( \sqrt[3]{x} = x^{\frac{1}{3}} \). The common definition of the cube root of a negative number is that
(-x)1/3 = -(x1/3).[1] For example:

• The cube root of -27 is written as \( \sqrt[3]{-27} = -3 \).
• The cube root of -8 is written as \( \sqrt[3]{-8} = -2 \).
• The cube root of -64 is written as \( \sqrt[3]{-64} = -4 \).

Cube roots (for integer results 1 through 10)

• Cube root of 1 is 1
• Cube root of 8 is 2
• Cube root of 27 is 3
• Cube root of 64 is 4
• Cube root of 125 is 5
• Cube root of 216 is 6
• Cube root of 343 is 7
• Cube root of 512 is 8
• Cube root of 729 is 9
• Cube root of 1000 is 10

To calculate fractional exponents use our calculator for Fractional Exponents.

References

[1] Weisstein, Eric W. "Cube Root." From MathWorld -- A Wolfram Web Resource. Cube Root

Math is Fun Cube Roots

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.

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

What is the 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.

How to Calculate the Value of the Cube Root of 64?

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 3: Use the law of exponents: 64 = 23 × 23 = 43
• 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.

Is the Cube Root of 64 Irrational?

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:

Cube Root of 64 Solved Examples

1. Example 1: Find the real root of the equation x3 − 64 = 0.

   Solution:

   x3 − 64 = 0 i.e. x3 = 64 Solving for x gives us, x = ∛64, x = ∛64 × (-1 + √3i))/2 and x = ∛64 × (-1 - √3i))/2 where i is called the imaginary unit and is equal to √-1. Ignoring imaginary roots, x = ∛64

   Therefore, the real root of the equation x3 − 64 = 0 is for x = ∛64 = 4.

Show Solution >

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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 = -43
• Take 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.

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.