Lesson 15

Irrational Numbers

  • Let’s explore irrational numbers

15.1: Finding a Home for Irrational Numbers

Number line from negative 5 to 5, by ones.

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.

  1. Right triangle. Base is 2, height is 3, hypotenuse is x.
  2. Right triangle. Base = 5. Height = 9. Hypotenuse = \(x\).
  3. Right triangle. Base is x, height is 10, hypotenuse is 12.
  4. Right triangle. Base is square root of 6, height is square root of 10, hypotenuse is x.
  5. Right triangle. Base is 7, height is x, hypotenuse is square root of 98.

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

Summary