# Lesson 3

Squares and Equations

• Let’s explore squares

### 3.1: Math Talk: Squaring Values

Mentally evaluate each expression.

$$7^2$$

$$(\text{-}7)^2$$

$$\text{-}7^2$$

$$(\text{-}\frac{2}{5})^2$$

### 3.2: Squares with Squares

Let $$p^2 = q$$

1. Select all pairs of values that could be $$p$$ and $$q$$.
• $$p = 6, q = 36$$
• $$p = \text{-}6, q = 36$$
• $$p = \text{-}2, q = \text{-}4$$
• $$p = \text{-}10, q = 100$$
• $$p = \frac{1}{2}, q = \frac{1}{4}$$
• $$p = \text{-}0.2, q = 0.4$$
2. List one other possible pair of values for $$p$$ and $$q$$ that make the equation true.
3. Use the diagrams to find the value of the side length for each square, then find the value for $$x$$.

1. The square has an area of 25.

2. The square has an area of 36.

3. The square has an area of 100

### 3.3: Matching Solutions and Equations

Here are some equations and a list of numbers. Which numbers are solutions to which equations?

1. $$c^2 = 121$$
2. $$5 \boldcdot d^2 = 500$$
3. $$80 = m^2 - 1$$
4. $$100 = (n + 3)^2$$
• -13
• -11
• -10
• -9
• -7
• 7
• 9
• 10
• 11
• 13