Ghanmul Question: Class 8 Maths Cube and Cube Roots Quiz and Flashcards

Questions and Answers

What is the volume of a cube with sides of length 5 units?

$125$ cubic units

What does the cube root of a number represent?

The number that, when multiplied by itself three times, gives the original number

Which property states that the cube of the sum or difference of two numbers is equal to the sum or difference of their cubes?

Associative Property

If a number is raised to the power of $3$, what operation does it represent?

Exponentiation Signup and view all the answers

What is the cube root of $64$?

$8$ Signup and view all the answers

What is the result when a number is cubed?

The number multiplied by itself three times Signup and view all the answers

What does the Identity Property for Cube Roots state?

Every positive number has a unique cube root Signup and view all the answers

Which property states that for any number a, a³ = a³?

Reflexive Property Signup and view all the answers

How can the cube root of a number be found using the Cubing Method?

By finding three numbers that multiply to give the given number Signup and view all the answers

Which property states that for any numbers a and b, if a³ = b³, then a = b?

Cube Root Property Signup and view all the answers

What does the Transitive Property state for cube roots?

If a³ = b³ and b³ = c³, then a³ = c³ Signup and view all the answers

What is the Long Division Method used for in finding cube roots?

Dividing the given number by a power of 3 repeatedly Signup and view all the answers

What does the Cube Property state regarding cube roots?

For any numbers a and b, if a³ = b³, then a = √[b³] and a = √[c³] Signup and view all the answers

What is the purpose of the Trial and Error Method in finding cube roots?

Guessing a number and finding its cube Signup and view all the answers

According to the properties mentioned, what does 'a' represent in 'a³'?

A single value 'a' raised to the power of 3 Signup and view all the answers

What is the importance of understanding cubes and cube roots?

To develop skills necessary for advanced mathematics courses in the future Signup and view all the answers

Study Notes

Class 8 Maths: Understanding Cube and Cube Roots

In Class 8 Maths, students are introduced to new concepts and skills that help them better understand and solve problems related to mathematics. One of the key topics in this class is the study of cube and cube roots. In this article, we will delve into the world of cubes and cube roots, exploring their definitions, properties, and how to find cube roots of a number.

What are Cubes and Cube Roots?

A cube is a mathematical figure whose edges are equal and form a perfect cube shape. When the sides of the cube are of length a unit, then the cube describes a cube of volume (a x a x a) = a³ cubic units.

The cube root of a number is the number that, when multiplied by itself three times, gives the original number. In mathematical terms, if a is a real number, a³ is the cube of a, and ³√a is the cube root of a.

Properties of Cubes and Cube Roots

There are several properties associated with cubes and cube roots, including:

Associative Property: The cube of the sum or difference of two numbers is equal to the sum or difference of their cubes: (a + b)³ = a³ + 3a²b + 3ab² + b³ and (a - b)³ = a³ - 3a²b - 3ab² + b³.
Distributive Property: The cube of the product of two numbers is equal to the product of their cubes: (ab)³ = a³b³.
Identity Property for Cube Roots: Every positive number has a unique cube root. If a is a positive number, then there exists a unique number x such that a = x³.
Identity Property for Cubes: Every positive number has a unique cube. If a is a positive number, then there exists a unique number x such that a = x³.
Reflexive Property: For any number a, a³ = a³.
Symmetric Property: For any numbers a and b, a³ = b³ if and only if a = b.
Transitive Property: For any numbers a, b, and c, if a³ = b³ and b³ = c³, then a³ = c³.
Cube Root Property: For any numbers a and b, if a³ = b³, then a = b.
Cube Property: For any numbers a, b, and c, if a³ = bc, then a = √[b³] and a = √[c³].

Finding Cube Roots of a Number

To find the cube root of a number, you can use the following methods:

Long Division Method: This method involves dividing the given number by a power of 3 repeatedly until the divisor is 1. Then, the quotient is the cube root of the given number.
Cubing Method: This method involves finding three numbers that, when multiplied together, give the given number. Then, the cube root of the given number is the average of these three numbers.
Trial and Error Method: This method involves guessing a number and then finding its cube. If the cube is not the given number, adjust the guess and try again until the cube is the given number.

Practice Problems

Find the cube of the following numbers: a. 2 b. 3 c. 4 d. 5
Find the cube root of the following numbers: a. 3 b. 8 c. 27 d. 125

Conclusion

Cubes and cube roots are essential mathematical concepts that students learn in Class 8 Maths. By understanding the properties of cubes and cube roots and learning how to find cube roots of a number, students can develop the skills necessary to solve more complex mathematical problems. This knowledge will also prepare them for more advanced mathematics courses in the future.