Surds

• How many rules are there for manipulating surds?


  6 rules
• What is the first rule for manipulating surds?


  1. $\sqrt{a} \times \sqrt{b} =$$\sqrt{ab}$

  • Example: $\sqrt{2} \times \sqrt{3} =$$\sqrt{6}$
• What is the second rule for manipulating surds?


  1. $\frac{\sqrt{a}}{\sqrt{b}} =$$\sqrt{\frac{a}{b}}$

  • Example: $\frac{\sqrt{8}}{\sqrt{2}} =$$\sqrt{4} =$$2$
• What is the third rule for manipulating surds?


  1. $\sqrt{a} +$$\sqrt{b} \text{ – DO NOTHING}$

  • It is NOT $\sqrt{a} +$$b$
• What is the fourth rule for manipulating surds?


  1. $(\sqrt{a} +$$\sqrt{b})(\sqrt{a} - \sqrt{b}) =$$a - b$

  • NOT just $a^2 - b^2$
• What is the fifth rule for manipulating surds?


  1. $(\sqrt{a} +$$\sqrt{b})^2 =$$a +$$2\sqrt{ab} +$$b$
• What is the sixth rule for manipulating surds?


  1. $\frac{a}{\sqrt{b}} =$$\frac{a\sqrt{b}}{b}$

  • This is known as ‘RATIONALISING the denominator’
• What does it mean to rationalize the denominator?


  It means to eliminate the square root from the bottom of the fraction.
• How do you rationalize denominators of the form $\sqrt{a} \pm \sqrt{b}$?


  • Multiply by the denominator
  • Change the sign in front of the root
• How do you simplify $\sqrt{300} +$$\sqrt{48} - 2\sqrt{75}$ in terms of $\sqrt{3}$?


  It simplifies to $4\sqrt{3}$.
• What is the area of a rectangle with length $4x$ cm and width $x$ cm if the area is $32 \text{ cm}^2$?


  The area is given by $4x^2 =$$32$.
• What is the exact value of $x$ when $4x^2 =$$32$?


  $x =$$2\sqrt{2}$
• How do you write $\frac{3}{2 + \sqrt{5}}$ in the form $a +$$b\sqrt{5}$?


  By rationalizing the denominator to get $-6 +$$3\sqrt{5}$.
• What are the exam practice questions provided in the material?


  1. Simplify $\sqrt{180} +$$\sqrt{20} +$$\sqrt{5}$
  2. Write $\frac{2}{\sqrt{5}}$ in the form $a +$$b\sqrt{5}$