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