# Lesson 15

Irrational Numbers

- Let’s explore irrational numbers

### 15.1: Finding a Home for Irrational Numbers

- \(\sqrt{5}\)
- \(\text{-}\sqrt{13}\)
- \(3+\sqrt{2}\)
- \(3-\sqrt{2}\)

### 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.

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