Simplifying Radical Expressions

Review Material: Simplifying numerical radical expressions

  1.  \rhd Simplifying square roots (3:08) 5 \sqrt{117} = 5 \sqrt{3^2 \cdot 13} = 15 \sqrt{13} and 3 \sqrt{26} cannot be simplified.
  2.  \rhd  Simplifying square roots of fractions (4:40) \sqrt{\dfrac{1}{200}} = \dfrac{1}{10\sqrt{2}} = \dfrac{\sqrt{2}}{20}
  3.  \star Simplifying square roots \sqrt{\dfrac{1}{44}}
  4. \rhd Simplifying sums of radicals (4:41) He uses the correct |x| = \sqrt{x^2} rather than the (false) \sqrt{x^2} = x. Hooray!
    Solve:   \sqrt{2x^2} + 4\sqrt{8} + 3\sqrt{2x^2} + \sqrt{8} = (4|x| + 10)\sqrt{2}
  5.  \rhd Simplifying differences of radicals (5:45) 4 \sqrt[4]{81x^5} - 2\sqrt[4]{81x^5} - \sqrt{x^3} = 6|x| \sqrt[4]{x} - |x|\sqrt{x}  In this video he correctly remarks that “If x>0, there’s no need for the |x|.”
  6.  \star Simplifying square root expressions (with no variables) \sqrt{\dfrac{6^2}{95}}
  7. \rhd Introduction to rationalizing the denominator (10:17)  [Example 1] \dfrac{1}{2}
    [Example 2] \dfrac{7}{15}
    [Example 3] \dfrac{12}{2 - \sqrt{5}}  Sal shows why multiplying by \dfrac{\sqrt{5}}{\sqrt{5}} doesn’t help and why multiplying by \dfrac{2+\sqrt{5}}{2+\sqrt{5}} does — difference of squares!
    [Example 4] \dfrac{5y}{2\sqrt{y} - 5} = \dfrac{10}{4y-25}