Simplifying Square Roots: Key Concepts and Techniques

What is the inverse operation of an exponent?

• Root

• Subtraction

• Multiplication

• Addition

Which of the following is a perfect square?

• 15

• 25

• 30

• 35

Why do we rationalize the denominator?

• To make the fraction larger

• To eliminate the radical from the denominator

• To simplify the numerator

• To convert the fraction to a decimal

What is the square root of 81?

• 10

• 8

• 9

• 7

Which method involves breaking a number into its prime factors?

• Decimal method

• Prime factorization method

• Perfect square method

• Fraction method

What is the simplified form of the square root of 28 using the perfect square method?

• 4√7

• √14

• √28

• 2√7

What is the product property of radicals?

• √(a / b) = √a / √b

• √(a + b) = √a + √b

• √(a - b) = √a - √b

• √(a * b) = √a * √b

What is the simplified form of √45 using the perfect square method?

• √9

• 3√5

• 5√3

• √15

What is the simplified form of √126?

• 6√7

• 2√63

• √126

• 3√14

Using the formula V = √(16d), what is the velocity of a tsunami in 300 feet of water?

• 10√2

• 20√2

• 30√2

• 40√2