Simplifying Cube and Square Roots

The video tutorial explains how to simplify square and cube roots using prime factorization. It covers the process of breaking down numbers into prime factors, identifying pairs or groups of identical factors, and simplifying the roots. Examples include simplifying the square root of 72 and 864, and the cube root of 144 and 648. The tutorial concludes with a summary of the steps involved in simplifying both square and cube roots.

What is a radicand?

• A number that can be expressed as a fraction

• A number under a radical sign

• A number that is a perfect cube

• A number that is a perfect square

What is a prime factor?

• A factor that can be divided by 2

• A factor that is greater than 10

• A factor that is a composite number

• A factor that is a prime number

How can 72 be expressed using its prime factors?

• 2 x 2 x 3 x 3

• 2 x 2 x 2 x 3 x 3

• 2 x 2 x 2 x 2 x 3

• 2 x 3 x 3 x 3

What is the simplified form of the square root of 72?

• 6 root 2

• 4 root 3

• 5 root 2

• 8 root 2

What is the first step in simplifying the square root of a number?

• Add 10 to the number

• Factor the number into its prime factors

• Divide the number by 2

• Multiply the number by itself

What is the simplified form of the square root of 72?

• 4 root 3

• 6 root 2

• 8 root 2

• 5 root 2

How many threes are there in the prime factorization of 864?

• Five

• Four

• Three

• Two

What is the simplified form of the square root of 864?

• 12 root 6

• 10 root 6

• 14 root 6

• 16 root 6

What is the simplified form of the square root of 864?

• 10 root 6

• 12 root 6

• 14 root 6

• 16 root 6

What is the first step in simplifying the cube root of a number?

• Add 5 to the number

• Multiply the number by itself

• Divide the number by 3

• Factor the number into its prime factors