Cube Roots and Prime Factorization

The video tutorial explains how to find the cube root of negative 343. It begins by discussing the concept of cube roots and negative numbers, then moves on to the prime factorization of 343. The tutorial demonstrates how to factor out negative 1 and find the prime factors of 343, which are 7, 7, and 7. Finally, it shows how to calculate the cube root by multiplying these factors, resulting in negative 7. The video emphasizes understanding the mathematical process and verifying the solution.

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

• Negative 343 to the 3/3 power

• Negative 343 to the 1/2 power

• Negative 343 to the 2/3 power

• Negative 343 to the 1/3 power

If x cubed equals negative 343, what is x?

• The cube root of negative 343

• The square root of negative 343

• The fifth root of negative 343

• The fourth root of negative 343

What is the first step in finding the cube root of negative 343?

• Dividing 343 by 2

• Prime factorization of 343

• Subtracting 343 from itself

• Adding 343 to itself

Which prime number is a factor of 343?

• 7

• 5

• 2

• 3

What is 343 expressed as a product of its prime factors?

• 2 x 2 x 2

• 3 x 3 x 3

• 7 x 7 x 7

• 5 x 5 x 5

What is the cube root of negative 1?

• 1

• -1

• 2

• 0

How can the expression be rewritten using the prime factors of 343?

• Cube root of negative 1 times 3 times 3 times 3

• Cube root of negative 1 times 2 times 2 times 2

• Cube root of negative 1 times 7 times 7 times 7

• Cube root of negative 1 times 5 times 5 times 5

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

• -7

• -49

• 7

• 49

How can you verify the result of the cube root of negative 343?

• Multiply -7 by itself three times

• Multiply -7 by itself twice

• Multiply 7 by itself three times

• Multiply 7 by itself twice

What is the significance of the negative sign in the cube root calculation?

• It has no effect on the result

• It makes the result negative

• It makes the result zero

• It makes the result positive