Simplifying Radicals with the Factor Tree Method

What is the primary goal when simplifying radicals?

• To find the largest prime number within the radical

• To add all prime factors of the radicand

• To reduce the radicand to its smallest form

• To multiply the radicand by itself

Which of the following is a prime factorization step in simplifying radicals?

• Adding all prime numbers together

• Dividing the radicand by its smallest prime factor

• Multiplying the radicand by the smallest prime number

• Breaking down the radicand into prime factors using a factor tree

What does the factor tree method help identify in the process of simplifying radicals?

• Largest prime number

• Pairs of prime factors

• Sum of all factors

• Product of radicand and prime numbers

What prime factors does the square root of 75 break down into?

• 2, 3, and 5

• 3, 5, and 5

• 3, 3, and 5

• 2, 5, and 5

What is the significance of finding pairs in the factor tree method?

• Pairs indicate the radical cannot be simplified

• Pairs are multiplied together to simplify the radical

• Finding pairs is only necessary for cube roots

• Each pair represents a number that can be moved outside the radical

What is the simplified form of the square root of 120?

• 2 radical 15

• 3 radical 10

• 2 radical 30

• 4 radical 5

Why is the square root of 210 considered an anomaly in simplification?

• It has multiple pairs of prime factors

• It cannot be simplified further

• It simplifies to a whole number

• It only contains one prime factor

What is the final simplified form of the square root of 48?

• 2 radical 12

• 4 radical 3

• 6 radical 2

• 3 radical 4

How many pairs of 2s are found in the factor tree of 48?

• Three pairs

• Four pairs

• Two pairs

• One pair

What is the simplified form of the square root of 540?

• 6 radical 15

• 9 radical 5

• 12 radical 3

• 3 radical 20