Podcast
Questions and Answers
What is the cube root of 10648 using prime factorization?
What is the cube root of 10648 using prime factorization?
22
Which statement is true: A perfect cube does not end with two zeros or If square of a number ends with 5, then its cube ends with 25?
Which statement is true: A perfect cube does not end with two zeros or If square of a number ends with 5, then its cube ends with 25?
If square of a number ends with 5, then its cube ends with 25
Can you guess the cube root of 1,331 without factorization?
Can you guess the cube root of 1,331 without factorization?
11
Express 32832 as a sum of two cubes in two different ways.
Express 32832 as a sum of two cubes in two different ways.
Signup and view all the answers
State whether the statement 'The cube of a two digit number may have seven or more digits' is true or false.
State whether the statement 'The cube of a two digit number may have seven or more digits' is true or false.
Signup and view all the answers
What is the cube root of 46656 using prime factorization?
What is the cube root of 46656 using prime factorization?
Signup and view all the answers
Study Notes
Cube Roots and Prime Factorization
- The cube root of 10648 is 22, as calculated using prime factorization.
- 10648 can be expressed as 2 x 2 x 2 x 11 x 11 x 11, which is the same as (2 x 11)³.
Perfect Cubes
-
A perfect cube does not end with two zeros. This is because the cube of any number ending in 0 will also end in 000.
-
If the square of a number ends in 5, then its cube also ends with 25.
-
For example, 5² = 25 and 5³ = 125.
Cube Root Estimation
- The cube root of 1,331 is 11. This can be guessed by knowing that 10³= 1000 and 12³= 1728, and 1331 falls between these two numbers.
Sum of Cubes
- 32832 can be expressed as the sum of two cubes in two different ways:
- 32832 = 32³ + 16³
- 32832 = 30³ + 28³
Cube of Two-Digit Numbers
- The statement 'The cube of a two-digit number may have seven or more digits' is false.
- The cube of a two-digit number will always have five or six digits. For example, the cube of 99 is 970299, which has six digits.
Cube Root of 46656
- The cube root of 46656 is 36, obtained by prime factorization.
- 46656 can be expressed as 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3, which is (2 x 3 x 3)³ = 36³.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Practice calculating cube roots of numbers using the given example in the textbook. Understand the process of forming groups of three digits from right to left and determining the cube root step by step.
