## Saturday, April 11, 2020

### Casio fx-CG 50 Update and Mental Math: Squaring a Number Ending in 5

Casio fx-CG 50 Update and Mental Math:   Squaring a Number Ending in 5

Casio fx-CG 50 Update

Casio released an update to the operating software for the fx-CG 50, version 3.40.   This update, among other things, expands the number of commands in Casio's Micropython.

There is a new module casioplot module has commands to draw pixels in any color and strings.

Click on Graphing Models.

I have not had a chance to try the new drawing commands yet, it's on my list of things to do.

Mental Math:   Squaring a Number Ending in 5

Squaring a positive integer whose last digit is 5 will result in the answer whose last digits are 25.

Why is this true?

Let n be a positive integer whose last digit is 5.   (n = 15, 25, 35, etc.).

Let m = n - 5, then n = m + 5.   Note that m is a multiple of 10.

Then:

n^2 = (m + 5)^2
= m^2 + 2 * m * 5 + 25
= m^2 + 10 * m + 25
= (m^2 + 10 * m) + 25
= m * (m + 10) + 25

Since m is a multiple of 10, m^2 and 10 *  m are multiples of 100.  Because of this fact, squaring integers ending in 5 is used in mental math.

Examples

Example 1:  Calculate 45^2.

n = 45 = 40 + 5    (m = 40)
= (40 + 5)^2
= 40 * (40 + 10) + 5^2
= 40 * 50 + 25
= 2000 + 25
= 2025

45^2 = 2025

Example 2:  Calculate 165^2

n = 165 = 160 + 5    (m = 160)
= (160 + 5)^2
= 160 * (160 + 10) + 25
= 160 * 170 + 25
=  27200 + 25
=  27225

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

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