Simplifying Radicals Through Prime Factorization

Mr. Maisonette's tutorial teaches how to express the square root of a number in its simplest radical form using prime factorization. The video provides three examples: simplifying √424, √936, and √1250. Each example involves breaking down the number into prime factors, identifying pairs to form perfect squares, and expressing the result in simplest radical form.

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

• Multiply the number by itself

• Divide the number by 2

• Subtract 1 from the number

• Find the prime factorization of the number

What is a prime number?

• A number that ends in 0

• A number that is a perfect square

• A number that can be divided by 2

• A number with exactly two factors: 1 and itself

What is the prime factorization of 424?

• 2 × 2 × 2 × 53

• 2 × 2 × 106

• 2 × 2 × 2 × 53

• 2 × 2 × 2 × 53

What is the simplest radical form of √424?

• 2√53

• 8√53

• 2√106

• 4√53

What is the prime factorization of 936?

• 2 × 2 × 2 × 3 × 3 × 13

• 2 × 2 × 2 × 3 × 3 × 13

• 2 × 2 × 2 × 3 × 3 × 13

• 2 × 2 × 2 × 3 × 3 × 26

What is the simplest radical form of √936?

• 3√26

• 4√26

• 6√13

• 6√26

What is the prime factorization of 1250?

• 2 × 5 × 5 × 25

• 2 × 5 × 5 × 5 × 5

• 2 × 5 × 5 × 25

• 2 × 5 × 5 × 5 × 5

What is the simplest radical form of √1250?

• 10√25

• 5√50

• 25√2

• 20√5

Why do we pair prime numbers when simplifying square roots?

• To simplify multiplication

• To find the greatest common divisor

• To create perfect squares

• To make the process faster

What is the final step in simplifying a square root?

• Dividing by the smallest prime factor

• Finding the square root of the perfect squares

• Multiplying the remaining numbers

• Adding all the prime factors