Simplifying Radicals through Prime Factorization

What is another term for a radical in mathematics?

• Variable

• Exponent

• Coefficient

• Square root

Why do we simplify radicals?

• To make them easier to calculate by hand

• To get a rounded decimal answer

• To write the answer in exact form

• Because it's required by mathematical laws

What is the first step in simplifying a radical?

• Make a factor tree

• Identify pairs of numbers

• Find the square root

• Divide by the smallest prime number

What do you do with pairs of numbers in a factor tree when simplifying radicals?

• Leave them under the radical

• Take one out of the radical

• Multiply them

• Add them together

How do you simplify the square root of 80?

• 2 radical 10

• 4 radical 5

• 16

• 8 radical 2

What does the prime factorization of a number help with in simplifying radicals?

• Finding pairs of numbers

• Calculating the decimal equivalent

• Reducing the number to its smallest prime

• Determining the largest factor

Why is it important to leave numbers without pairs under the radical when simplifying?

• To increase the value of the radical

• To make the calculation easier

• Because they cannot be simplified further

• To ensure the answer is in its simplest form

What is the simplified form of the square root of 128?

• 4 radical 4

• 8 radical 2

• 2 radical 64

• 16 radical 2

How is the square root of 75 simplified when involving variables?

• 5 radical 75x

• 75x

• 3x radical 5x

• 5x radical 3x

What is the result of simplifying the radical expression of 75x to the third power?

• 5x radical 3x

• 5x squared radical 3

• 3x squared radical 5

• 15x radical 5