Okay, let’s break down the cube root of 64. A cube root is just a number that, when you multiply it by itself three times, gives you the original number. So, what is it? The cube root of 64 is 4!
One of the most common ways to figure this out is by using prime factorization.
Understanding Cube Roots
Let’s talk about cube roots and how they work.
Definition and notation
The cube root of a number, which we’ll call x, is written as ∛x. Think of it this way: finding the cube root is the opposite of cubing a number.
Perfect cubes
A perfect cube is a number you get when you cube an integer. For example, 64 is a perfect cube because 4 x 4 x 4 = 64.
So, what does this have to do with 3/64? We’ll get there. First, we need to understand fractions.
Prime Factorization Method to Find the Cube Root of 64
Prime factorization is a way of breaking down a number into its prime number components. Let’s use this method to find the cube root of 64.
- First, we break down 64 into prime factors: 64 = 2 × 2 × 2 × 2 × 2 × 2.
- Next, we group the prime factors into sets of three: (2 × 2 × 2) × (2 × 2 × 2).
- Since we have two groups of (2 × 2 × 2), we know the cube root is 2 x 2 = 4.
This can be expressed with exponents like this: 64 = 26 = (2²)³ = 4³
Using Cube Roots in the Real World
Understanding cube roots is surprisingly useful. They pop up in all sorts of places, from calculating the volume of a 3D object to complex engineering problems.
Think of it this way: if you have a cube-shaped box, and you know it holds 64 cubic inches of stuff, then each side of the box is the cube root of 64 inches long. That’s 4 inches.
You can use a cube root table to quickly figure out the cube root of common perfect cubes.
To Conclude
So, to recap, the cube root of 64 is 4. We found this by using prime factorization, a reliable method for figuring out the cube roots of perfect cubes.
Understanding cube roots is more than just a math problem; it’s a fundamental skill that has practical applications in many areas of life.