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      Square Root on Your Computer's Calculator

Your Computer's Calculator  

    This page has two purposes -- to explain the mathematics of square roots and to explain how to use the calculator to obtain the exact root or an approximation of the root.

    Two sets of background material gets you ready for this task -- the math definitions and vocabulary and other calculator functions or buttons.

    To review the math, visit: Powers of Ten, powers, principal root, square, square root, radical, radical sign, and radicand.

    Keep both notes open and your calculator open.


    Use your CALCULATOR Button to view an picture of the computer's calculator.

The Square Root  

    Compute mentallly the square roots in the first two examples. Then, use your computer's calculator to complete each example so you see how the calculator works.

    To take a square root you must:
  • Enter the initial number
  • Press []

Example #1: The square root of 25



Example #2: The square root of 4


"A Horse of A Different Color"  

    "A Horse of A Different Color" is an expression used in a situtation in which, though one knows a great deal about one situtation, the situation at hand is different enough to be thought of as a completely different situation.


Example #3: Simplify:

  • [4], to begin to write -4
  • [+/-], to change the sign and write -4,
  • [], to take the square root
  • an error message appears on the calculator -- "invalid input for function"
  • 2i, the imaginary and complex number is the correct principal square root of -4

    What this means is this calculator can not "speak" all languages humans use when they do math. This calculator can not preform the required work -- it is not made for this purpose. A scientific or graphing calculator which uses complex numbers is required.


Another Example: "Someone's Using the Upstairs John"  

    You know ... "Someone's Using the Upstairs John" -- the high pot in use -- the hypotenuse -- that thing with the Pythagorean Theorem.

    You can probably complete this example mentally. See how much more work is required when the calculator does the arithmetic.


Example #4: Find the hypotenuse or a right triangle which has sides of 3 units and 4 units.

  • Recall: a² + b² = c²
  • Restate with the current information:   3² + 4² = c²
  • So, with calculator find: c = +
  • [3][x][3][=], to get 9
  • [MS], to store the 9
  • [4][x][4][=], to get 16
  • [M+] to get add this to the Memory
  • [MR], to recall the stored sum, 25
  • [], to take the square root
  • 5 is the principal square root of 25
  • The hypotenuse is 5 units in length.


The One-Half Power

    Square and square root are inverse operations - one undoes the other. The exponential notation, or powers, used to indicate each are deliberately reciprocals of each other.

To square, raise to the second power -- the 2 power.
To square root, raise to the one-half power -- the 1/2 power.
To cube, raise to the third power -- the 3 power.
To cube root, raise to the 1one-third power -- the 1/3 power.
To "undo" a fourth power, use the one-fourth power --
1/4 power "undoes" the 4 power.
To "undo" a fifth root, use the fifth power --
the 5 power "undoes" the 1/5 power.
Example #5: Squaring a Square Root to Obtain
the Original Number
Choose any positive number, including decimals
-- and type it into the calculator.
Press [], the square root key
-- to obtain the square root.
Press [MS], the store in memory key
-- to save the decimal approximation of the number.
You now know both:
Press [x] then [MR] then [=]
-- to multiply the displayed root by itself.
-- The square of a square root is the original number.

    Next we expand the list of some of the powers of two so that the one-half powers are also included.


Example #6: Even More Powers of Two

  • is , 2 to the zero
  • is , the square root of 2
  • is 2 to the first
  • is , 2 times the square root of 2
  • is , 2 squared
  • is , 2 squared times the square root of 2
  • is
  • 2 cubed
  • is , 2 cubed times the square root of 2
  • is , 2 to the fourth


    So, raising a number to the one-half power means taking its square root.

    Next, return to pg 7 of FINALLY PLEASE READILY EXCUSE MY DEAR AUNT SALLY!, Order of Operations.


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