How to use prime factorization to determine the square root of a number, sqrt(56)

The video tutorial explains how to simplify the square root of 56 by using prime factorization. The teacher guides students through identifying integer pairs and applying prime factorization to break down the number into its prime factors. The concept of simplifying square roots by identifying pairs is emphasized, and the properties of square roots are discussed to help students understand the process. The tutorial concludes with a practical problem for students to solve.

What is the main reason 56 cannot be expressed as a product of two identical integers?

• Because 56 is a composite number.

• Because 56 is not a perfect square.

• Because 56 is an even number.

• Because 56 is a prime number.

What is the first step in the prime factorization of 56?

• Divide by 3.

• Divide by 2.

• Divide by 5.

• Divide by 7.

After dividing 56 by 2 three times, what are the prime factors obtained?

• 2, 2, 3, 7

• 2, 3, 3, 7

• 2, 2, 2, 5

• 2, 2, 2, 7

Why can the square root of 2 * 2 be simplified to 2?

• Because 2 * 2 equals 8.

• Because 2 * 2 equals 5.

• Because 2 * 2 equals 4, which is a perfect square.

• Because 2 * 2 equals 6.

Why do the numbers 2 and 7 remain under the square root in the expression sqrt(56)?

• Because they are both even numbers.

• Because they do not form a pair.

• Because they are both odd numbers.

• Because they are both prime numbers.