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 $\frac{a}{b}=\frac{c}{d}$, where $b \neq 0, d \neq 0$, then $a \cdot d = b \cdot c$.
• Square root property: If $x^2=k$, then $x = \pm \sqrt{k}$
  • If $k>0$ the equation has two solutions
  • If $k=0$ the equation has one solution
  • If $k<0$ the equation has no solution
• We can remove a radical from an equation using the following two properties:
  • if $a=b$ then $a^2 = b^2$
  • for $x \geq 0, (\sqrt{x})^2=x$
• 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 $\frac{a}{b}=\frac{c}{d}$, where $b \neq 0, d \neq 0$

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

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