Simplifying Radical Expressions

This video tutorial introduces the concept of simplest radical form, focusing on numbers without variables. It explains the process of simplifying radicals by breaking them into products of perfect squares and non-perfect squares. The tutorial provides step-by-step examples, including √24, √48, √72, √396, √175, and √162, demonstrating both correct and incorrect methods. Viewers are encouraged to practice with additional problems.

Why is it important to have a calculator for this lesson?

• To check the answers at the end

• To divide numbers under the radicands by perfect squares

• To add and subtract numbers

• To multiply large numbers

What is the term used for the symbol under which numbers are placed in simplest radical form?

• Perfect square

• Square root

• Radicand

• Radical

What is the first step in simplifying a number under a radical?

• Breaking it into the product of two numbers, one of which is a perfect square

• Subtracting a perfect square from it

• Adding the number to a perfect square

• Multiplying it by another number

What is the simplest radical form of the square root of 24?

• 2√6

• 4√6

• 3√8

• 6√2

When simplifying the square root of 48, what is the largest perfect square that divides 48?

• 25

• 16

• 9

• 4

What is the correct simplest radical form of the square root of 72?

• 3√24

• 4√18

• 6√2

• 2√18

What is the first step in finding the simplest radical form of the square root of 396?

• Subtract a perfect square from 396

• Multiply 396 by a perfect square

• Find the largest perfect square less than or equal to half of 396

• Divide 396 by 2

What is the simplest radical form of the square root of 175?

• 5√25

• 7√5

• 5√7

• 25√7

What is the simplest radical form of the square root of 162?

• 6√3

• 8√2

• 9√2

• 3√18

What should you do if you cannot find a perfect square that divides a number evenly?

• Subtract 1 from the number

• Divide the number by 3

• Circle the original number under the radical

• Multiply the number by 2