Exploring Radicals and Quadratic Equations

This video tutorial reviews simplifying radicals and solving quadratic equations, focusing on methods using perfect squares. It covers simplifying radicals, adding and subtracting radicals, and multiplying radicals, with detailed examples for each. The tutorial emphasizes solving by hand but mentions a calculator program for class use.

What is a perfect square?

• A number that can be expressed as the difference of two identical integers

• A number that can be expressed as the quotient of two identical integers

• A number that can be expressed as the product of two identical integers

• A number that can be expressed as the sum of two identical integers

How do you simplify the square root of 50?

• 5 square root of 2

• 25 square root of 2

• 5 square root of 10

• 10 square root of 5

What is the simplified form of negative 5 times the square root of 72?

• -36 square root of 2

• -30 square root of 3

• -25 square root of 2

• -30 square root of 2

Can you add square root of 72 and 5 square root of 8 directly?

• No, because one is negative

• Yes, because they are both multiples of 4

• Yes, because they are both square roots

• No, because they have different numbers under the radical

What is the result of adding 6 square root of 2 and 10 square root of 2?

• 20 square root of 2

• 4 square root of 2

• 16 square root of 2

• 16 square root of 4

What is the simplified result of multiplying the square root of 8 by the square root of 5?

• 2 square root of 10

• 4 square root of 10

• Square root of 13

• Square root of 40

What do you get when you square the square root of 11?

• 121

• Square root of 11

• 11

• Square root of 121

How do you handle a radical squared in calculations?

• Subtract the number under the radical from itself

• Write the radical twice and multiply

• Add the number under the radical to itself

• Multiply the number under the radical by itself

What is the result of distributing 3 outside the radical over (square root of 2 times 5 + square root of 8 times 2)?

• 15 square root of 10 + 84

• 15 square root of 10 + 21 square root of 16

• 18 square root of 10 + 84

• 15 square root of 10 + 21 square root of 4

What is the final simplified form of 49 times the square root of 4?

• 2

• 98

• 49

• 196