Math

• What is a surd?

  A square root that cannot simplify to a whole number
• Why is $\sqrt{2}$ considered a surd?


  It cannot be simplified into a whole number
• How do you simplify surds?

  • Find a square number factor
  • Example: $\sqrt{50} =$$\sqrt{25 \times 2} =$$5\sqrt{2}$
• How do you multiply surds?

  Multiply the numbers inside the square root
• How do you divide surds?

  Divide the numbers inside the square root
• What is the rule for adding and subtracting surds?

  • Only like surds can be added or subtracted
  • Example: $3\sqrt{2} +$$5\sqrt{2} =$$8\sqrt{2}$
  • Example: $4\sqrt{3} +$$2\sqrt{5}$ cannot be simplified
• How do you expand brackets with surds?

  Use FOIL: First, Outer, Inner, Last
• How do you rationalize the denominator?

  • Remove the surd from the denominator
  • Multiply top & bottom by the surd
  • Example: $\frac{5\sqrt{3}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} =$$\frac{5\sqrt{3}}{3}$
• How do you rationalize a two-term denominator?

  • Multiply by the conjugate
  • Change the sign in the middle
  • Example: $\frac{3}{2+\sqrt{5}} \times \frac{2-\sqrt{5}}{2-\sqrt{5}}$