Simplifying Square Roots Concepts

This lesson focuses on simplifying square roots, starting with perfect squares and moving to non-perfect squares. It introduces a method to rewrite square roots in a simplified form without approximation. The lesson includes a mathematical proof of the method and provides several examples and exercises for practice. Advanced examples demonstrate the use of factorization in simplification.

What is the main focus of Lesson Four in Module 7?

• Approximating square roots

• Simplifying square roots without approximation

• Estimating square roots

• Learning about cube roots

How can the square root of 20 be rewritten using factors?

• As the square root of 10 * 2

• As the square root of 5 * 4

• As the square root of 2 * 10

• As the square root of 4 * 5

What is the purpose of proving the method for simplifying square roots?

• To show that square roots can be approximated

• To demonstrate the equality of expressions

• To find the exact value of square roots

• To learn about cube roots

Which of the following is a simplified form of the square root of 50?

• 5 * square root of 2

• Square root of 50

• Square root of 25 * 2

• 7 * square root of 2

How can the square root of 28 be simplified?

• As the square root of 4 * 7

• As the square root of 28

• As the square root of 7 * 4

• As the square root of 14 * 2

What is a key strategy for simplifying square roots of larger numbers?

• Ignoring perfect squares

• Estimating the square root

• Finding prime factorization

• Using a calculator

What is the simplified form of the square root of 75?

• 5 * square root of 3

• Square root of 25 * 3

• Square root of 75

• 3 * square root of 5

Which method can be used to find all perfect square factors of a number?

• Guessing

• Prime factorization

• Approximating

• Using a calculator

What is the simplified form of the square root of 200?

• Square root of 50 * 4

• Square root of 100 * 2

• 10 * square root of 2

• 5 * square root of 4

What is the simplified form of the square root of 504 using prime factorization?

• 7 * square root of 72

• Square root of 126 * 4

• Square root of 252 * 2

• 6 * square root of 14