Problem 63 To help find cube roots, complet... [FREE SOLUTION]

91影视

Chapter 10: Problem 63

To help find cube roots, complete this list of perfect cubes. $$1^{3}=\quad 2^{3}=\quad 3^{3}=\quad 4^{3}=\quad 5^{3}=$$ $$6^{3}=\quad 7^{3}=\quad 8^{3}=\quad 9^{3}=\quad 10^{3}=$$

Short Answer

Expert verified

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Step by step solution

- Calculate the first perfect cube

Calculate the cube of 1: \[1^3 = 1 \cdot 1 \cdot 1 = 1\]

- Calculate the second perfect cube

Calculate the cube of 2: \[2^3 = 2 \cdot 2 \cdot 2 = 8\]

- Calculate the third perfect cube

Calculate the cube of 3: \[3^3 = 3 \cdot 3 \cdot 3 = 27\]

- Calculate the fourth perfect cube

Calculate the cube of 4: \[4^3 = 4 \cdot 4 \cdot 4 = 64\]

- Calculate the fifth perfect cube

Calculate the cube of 5: \[5^3 = 5 \cdot 5 \cdot 5 = 125\]

- Calculate the sixth perfect cube

Calculate the cube of 6: \[6^3 = 6 \cdot 6 \cdot 6 = 216\]

- Calculate the seventh perfect cube

Calculate the cube of 7: \[7^3 = 7 \cdot 7 \cdot 7 = 343\]

- Calculate the eighth perfect cube

Calculate the cube of 8: \[8^3 = 8 \cdot 8 \cdot 8 = 512\]

- Calculate the ninth perfect cube

Calculate the cube of 9: \[9^3 = 9 \cdot 9 \cdot 9 = 729\]

- Calculate the tenth perfect cube

Calculate the cube of 10: \[10^3 = 10 \cdot 10 \cdot 10 = 1000\]

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cube Roots

A cube root is a number that, when multiplied by itself three times, equals a given number. For example, the cube root of 27 is 3 because $3 \times 3 \times 3 = 27$. Understanding cube roots is essential to recognizing perfect cubes.

To find cube roots, you reverse the process of cubing a number.
If someone gives you a number, say 125, you need to find a number which, when cubed, results in 125.
Here, the cube root of 125 is 5 because $5^3 = 125$.

Practicing finding cube roots helps you decode complex problems involving powers and roots.

Exponents

Exponents are a way of representing repeated multiplication of the same number by itself. In our context, we specifically deal with cubes, which means using the exponent 3.

For example, $3^3$ means multiplying 3 by itself three times: $3\times 3 \times 3 = 27$.
This is unlike squaring a number, which uses an exponent of 2.
Understanding exponents simplifies calculation and notation, letting you express large numbers concisely.

Recognizing and working with exponents becomes much easier with practice and understanding how to execute these multiplications.

Multiplication

Multiplication is a basic arithmetic operation that combines groups of the same size. When calculating cubes, you perform multiplication multiple times with the same number.

For instance, $4^3 = 4 \times 4 \times 4$ shows three multiplications with the number 4.
Mastering this concept allows tackling cubes and cube roots smoothly since you need to multiply the number multiple times to get the perfect cube.
Practicing multiplication tables helps in quickly recognizing and solving cubes of numbers.

Understanding the process of multiplication, especially when repeated, is key to solving complex mathematical problems, including cubes and their roots.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.