Summary: Review

Key Concepts

  • A proportion can be solved by multiplying both sides by the lowest common denominator (LCD).
  • To solve a proportion by finding cross products:
    • If [latex]\frac{a}{b}=\frac{c}{d}[/latex], where [latex]b \neq 0, d \neq 0[/latex], then [latex]a \cdot d = b \cdot c[/latex].
  • Square root property: If [latex]x^2=k[/latex], then [latex]x = \pm \sqrt{k}[/latex]
    • If [latex]k>0[/latex] the equation has two solutions
    • If [latex]k=0[/latex] the equation has one solution
    • If [latex]k<0[/latex] the equation has no solution
  • We can remove a radical from an equation using the following two properties:
    • if [latex]a=b[/latex] then [latex]a^2 = b^2[/latex]
    • for [latex]x \geq 0, (\sqrt{x})^2=x[/latex]
  • To solve a radical equation:
    • Isolate the radical expression
    • Square both sides of the equation
    • Once the radical is removed, solve for the unknown
    • Check your solution

Glossary

extraneous solutions: solutions that do not create a true statement when substituted back into the original equation

proportion: a equation of the form [latex]\frac{a}{b}=\frac{c}{d}[/latex], where [latex]b \neq 0, d \neq 0[/latex]

quadratic equation: can be written [latex]ax^2+bx+c=0, a \neq 0, b \ \mathrm{and} \ c[/latex] are constants

radical equation: equation containing a radical such as a square root