PEDMAS, Exponents, Square Roots, and Perfect Squares

• Grouping symbols are things like parentheses, brackets, and fraction bars.
• Parentheses will require multiplication
• Using a fraction bar

  1. Work out numerator

  2. Work out denominator

  3. Then divide
• Order of operations


  The order that should be used to get the correct answer in mathematics
• PEMDAS


  A trick for memorizing the order of operations
• PEMDAS stands for

  • Parentheses
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction
• The Parentheses in PEMDAS refers to all grouping symbols, not just parentheses.
• Order of operations (step-by-step)

  1. Simplify grouping symbols

  2. Simplify exponents

  3. Multiply and divide

  4. Add and subtract
• Exponents are sometimes referred to as (base) to the (exponent) power
• An exponent of two is referred to as (base) squared
• An exponent of three is referred to as (base) cubed
• A number with an exponent of one is equal to that number.
• A number with an exponent of zero is equal to one.
• Scientific notation


  A way of making incredibly large or incredibly small numbers easier and less time consuming to write
• Perfect square


  The product of a whole number multiplied by itself
• A square root consists of a number beneath the radical symbol, called the radicand
• Root


  The answer to a square root equation
• Square root


  The number that can be multiplied by itself to equal the radicand
• A negative root is also technically correct. However if negatives have not been mentioned it can be assumed that they are asking for the positive answer
• Finding the square root of a fraction

  1. Find square root of numerator

  2. Find square root of denominator

  3. Rewrite as a new fraction
• Finding the square root of a decimal

  1. Convert decimal into fraction form

  2. Find the square root
• If the first number is a decimal when multiplying in scientific notation, move the decimal point to the right by the number of zeros in the second number
• If the exponent is negative when multiplying in scientific notation, move the decimal points to the left and place the zeros before the number
• Finding square roots of imperfect squares

  1. Find two perfect squares between which your number falls

  2. Round towards the closer number
• Base


  The number in an exponent that is being multiplied
• Exponent


  The digit representing the amount of times a number is being multiplied by itself
• If when finding the simplest radical form there are two whole numbers not within the square root symbol multiply them
• Simplest Square Root

  1. Find two factors of the radicand, one of which must be a perfect square. 
  2. Write the factors separately as square roots.
  3. Simplify the perfect square and keep the other factor under its square root.
  4. If the remaining factor under the square root can be further simplified, repeat the process
  5. The final expression will have the root and square root.
• When writing your answer to a simplest square root equation don’t forget to write the integer in front of the square root
• What is a coefficient?

  A coefficient is a number that is equal to or more than one and less than ten
• When turning a number into a coefficient place a decimal to the right of the number and move it left until it fits the requirements of a coefficient
• Every time you move the decimal to the left to make a coefficient you also need to raise the value of the exponent by one
• Dividing in scientific notation

  1. Divide the coefficients by each other. The numerator by the denominator.
  2. Subtract the exponents. 
  3. The answer will be “coefficient x base” (and exponent).
• When dividing in scientific notation the numbers will be separated by a fraction bar
• A number is written in scientific notation when a coefficient is being multiplied by a power of ten
• Multiplying in scientific notation

  1. Multiply the coefficients.
  2. Add the exponents.
  3. If the result is ten or greater covert it back into a coefficient.
  4. The answer will be “coefficient x base” (and exponent).