Cube Roots and Divisibility Concepts

The video tutorial explains how to find the cube root of negative 343. It begins by expressing the problem in different ways, such as finding a number that multiplies by itself three times to give -343 or raising -343 to the 1/3 power. The tutorial then factors -343, starting with factoring out -1 and checking divisibility by numbers 2 through 7. It identifies 7 as a prime factor, leading to the expression of -343 as -1 times 7 cubed. The cube root is then calculated as negative 7, with verification steps included.

What is another way to express finding the cube root of negative 343?

• Raising negative 343 to the 1/2 power

• Finding a number that multiplies by itself twice to get negative 343

• Raising negative 343 to the 1/3 power

• Finding a number that adds up to negative 343

What is the first step in factoring negative 343?

• Check divisibility by 5

• Factor out negative 1

• Multiply by 3

• Divide by 2

Why is 343 not divisible by 3?

• It is divisible by 2

• It is an even number

• The digits add up to 10, not a multiple of 3

• It ends with a 0

How do we confirm that 343 is divisible by 7?

• By dividing 343 by 7 and getting a whole number

• By multiplying 7 by 49

• By checking if it ends with a 7

• By adding the digits to get a multiple of 7

What is 49 factored into?

• 7 times 7

• 5 times 9

• 6 times 8

• 4 times 12

What is the cube root of negative 1?

• 3

• 1

• 0

• Negative 1

What is the cube root of 7 times 7 times 7?

• 21

• 7

• 14

• 49

What is the final result of the cube root of negative 343?

• Negative 7

• Negative 49

• 7

• 49

Which of the following is true about the cube root of negative 343?

• It is a fraction

• It is a positive number

• It is zero

• It is negative 7

What operation confirms the cube root of negative 343?

• Subtraction

• Multiplication

• Addition

• Division