# Lesson 15

Irrational Numbers

• Let’s explore irrational numbers

### 15.1: Finding a Home for Irrational Numbers

Use the number line to place these values in their approximate location.

1. $$\sqrt{5}$$
2. $$\text{-}\sqrt{13}$$
3. $$3+\sqrt{2}$$
4. $$3-\sqrt{2}$$

### 15.2: Solving for Missing Sides

For each triangle, use the Pythagorean Theorem to find the length of the missing side.

### 15.3: Solving with Square Roots

Solve each of these equations. Represent the solutions exactly. If the solution is not a whole number, what 2 whole numbers does each solution lie between? Be prepared to explain your reasoning.

1. $$(x+1)^2 = 64$$
2. $$(x-3)^2 - 4 = 0$$
3. $$x^2 = 10$$
4. $$(x-2)^2 = 12$$
5. $$(x+3)^2 = 24+4$$