Surds

• What are numbers that cannot be written as exact decimals or fractions called?

  Surds
• What is an example of a surd?


  $\sqrt{3}$
• If a square has an area of $3 \text{ m}^2$, what is the length of each side?


  Approximately $1.73 \text{ m}$
• How can $\sqrt{3}$ be expressed in decimal form?


  Approximately $1.732050807568877$
• What is the process to round $1.732050807568877$ to two decimal places?


  Round to $1.73$
• How can you check the area calculation of a square with side length $1.73 \text{ m}$?


  By calculating $(1.73 \text{ m})^2$
• What is the process for simplifying surds?


  • Identify square factors of the surd
  • Example: $\sqrt{12} =$$\sqrt{4 \times 3} =$$\sqrt{4} \times \sqrt{3} =$$2\sqrt{3}$
• What is the general rule for simplifying surds?


  $\sqrt{a} \times \sqrt{b} =$$\sqrt{ab}$
• How do you add $5\sqrt{2} - 3\sqrt{2}$?


  Combine to get $2\sqrt{2}$
• What happens when the square roots are the same in surd addition?


  You can combine the coefficients
• What is the result of $2\sqrt{5} +$$9\sqrt{5}$?


  $11\sqrt{5}$
• What is the result of $8\sqrt{3} +$$3\sqrt{5}$?


  Cannot be simplified further
• What is the result of $(\sqrt{3})^2$?


  $3$
• What is $(\sqrt{7})^2$?


  $7$
• How do you divide surds?


  By dividing the components separately
• What is the result of dividing $8\sqrt{6}$ by $2\sqrt{3}$?


  $4\sqrt{2}$
• What is rationalizing the denominator?


  • Simplifying a fraction with a surd in the denominator
  • Making the denominator an integer
  • Example: $\frac{\sqrt{8}}{6} =$$\frac{2\sqrt{3}}{3}$
• How do you simplify $\frac{\sqrt{8}}{6}$?


  $\frac{2\sqrt{3}}{3}$
• What is the first step in simplifying $\sqrt{8}$?


  Factor it as $\sqrt{4 \times 2}$
• What do you multiply by to rationalize $\frac{\sqrt{8}}{6}$?


  $\sqrt{6}$
• What is the final result of rationalizing $\frac{\sqrt{8}}{6}$?


  $\frac{2\sqrt{3}}{3}$