Simplifying Square Roots and Using Conjugates

The video tutorial covers simplifying square roots and using conjugates. It begins with a review of basic concepts and demonstrates how to simplify the square root of 50 using a factor tree. The tutorial then explains simplifying expressions with perfect squares, such as 4 and 64, by splitting the square root and reducing. Next, it breaks down the square root of 32, showing how to simplify it by identifying perfect squares and multiplying. Finally, the video addresses using conjugates to eliminate square roots from denominators, employing the FOIL method to simplify expressions.

What is the first step in simplifying the square root of 50?

• Divide by 5

• Use a factor tree

• Multiply by 2

• Add 25

When simplifying the square root of 50, which pair of numbers is used?

• 2 and 25

• 5 and 10

• 3 and 17

• 4 and 12

How can you simplify the expression involving the square root of 4 and 64?

• Add the numbers

• Multiply the numbers

• Subtract the numbers

• Split the square root and simplify each

What is the simplified form of the square root of 4 divided by the square root of 64?

• 1/4

• 2/8

• 1/2

• 4/8

In the expression 3 times the square root of 32, what is the simplified form of the square root of 32?

• 5 times the square root of 2

• 4 times the square root of 2

• 6 times the square root of 2

• 7 times the square root of 2

What is the result when you multiply 3 by the simplified square root of 32?

• 10

• 12

• 14

• 16

Why do we use conjugates when simplifying expressions with square roots in the denominator?

• To make the expression longer

• To increase the value

• To eliminate the square root

• To add more terms

What is the conjugate of 3 minus the square root of 5?

• 3 plus the square root of 5

• 3 minus the square root of 5

• 5 plus the square root of 3

• 5 minus the square root of 3

After using the conjugate, what is the simplified form of the denominator in the expression involving the square root of 5?

• 2

• 3

• 4

• 5

What is the final simplified form of the expression 21 plus 7 times the square root of 5 all over 4?

• 21/4 + 7 times the square root of 5/4

• 21/5 + 7 times the square root of 5/5

• 21/3 + 7 times the square root of 5/3

• 21/2 + 7 times the square root of 5/2