SQUARE ROOTS

WARM UP

1. Simplify the expression: 8b + 12(b + 2)

2. Write and solve the equation: twenty-one subtracted from a number is – 8. Find the number.

3. Write an equation for the function: x 1 2 3 4 5

y 5 10 15 20 25

While listening to the song, HIP TO BE SQUARE, brainstorm in your groups everything you know about squares.

http://www.youtube.com/watch?v=LB5YkmjalDg&feature=kp

1.2.3.4.5.

Each group will now receive a piece of squared paper.

In your groups, make the smallest square possible.What do you notice? What are the dimensions?What is the area?

Now, make the next smallest square possible. What do you notice? What are the dimensions? What is the area?

Continue to do this and record what you notice.

What does it mean to square a number?

What does it mean for a number to be a perfect square?

Can just any number be considered a square number? Why/why not?

https://www.youtube.com/watch?v=Ymcf14wC9Ck

https://learnzillion.com/lessons/182-identify-perfect-squares-and-find-square-roots

From your discovery, what can you tell me about the relationship between the side lengths of each square and the area?

1 x 1 = 1 8 x 8 = 64 15 x 15 = 225

2 x 2 = 4 9 x 9 = 8116 x 16 = 256

3 x 3 = 9 10 x 10 = 10017 x 17 = 289

4 x 4 = 16 11 x 11 = 12118 x 18 = 324

5 x 5 = 25 12 x 12 = 14419 x 19 = 361

6 x 6 = 36 13 x 13 = 16920 x 20 = 400

7 x 7 = 49 14 x 14 = 196

A perfect square is a number made by squaring a whole number.Example: 3 = 9 – 9 is a perfect square

4² = 16 – 16 is a perfect square 12² = 144 – 144 is a perfect square

Roots, or radicals, are the “opposite” or inverse of a perfect square. You “undo” a perfect square/power with a radical.

Eg: = 3 = 16 = = 12

The is called the “radical” symbol.

An answer to a root will often be written as ±. Why do you think this is? Take a few minutes to think about this. Then, share your ideas with your group. Each group must come up with one idea that they can share with the class.

Eg: = 5

THINK – PAIR - SHARE

 

1. = ____________ 2. = ______________

3. = ___________ 4. + = __________

5. = ____________ 6. + = ___________

7. = ___________ 8. = _____________

9. = ____________ 10. = ___________

Try these in your groups.

How do you think we can solve an equation using square numbers?

= 49

= 81

=

=

We can also use our knowledge of square roots and perfect squares to solve word problems.

You want to carpet a square room that has an area of 144 square feet. What is the length of one side of the room?

You have a blanket that has an area of 1600 square inches. What is the length of one side of the blanket?

Jenny’s square bedroom has an area of 90 square feet. The length of one side is between which two whole numbers. Find the length of one side.

Complete the worksheet. Show all your work. This is the first worksheet that you will add to your portfolio.

Complete the square root worksheet for homework.