Fast Math Squaring Numbers That End in 5

Squaring numbers that end in 5 are very easy and can be done very fast.

The fast math tricks have actually many different ways to solve but I will present 3.

1) Addition method:

Lets start with a number 55.
Subtract 5 from the original number: 55-5=50.

We will call this number our base number.

Square the base number: 50²=2500

Multiply the base number by 10: 10x50=500

Add the square of the base number to the base number x 10 and add 25: 2500+500+25=3025

If we wanted to find out what 115² equals, we would do the following:
115-5=110
110²=12100

110x10=1100
115²=12,100+1100+25=13,225

2) Subtraction method:

Lets start with a number 55 again.
Add 5 from the original number: 55+5=60.

We will call this number our base number.

Square the base number: 60²=3600

Multiply the base number by 10: 10x60=600

Subtract the base number x 10 from the base number squared and add 25: 3600-600+25=3025

Pretty cool so far right?

Lets use this methodology to find 95²

95+5=100
100²=10,000

100x10=1000
95²=10,000-1000+25=9025

3) Multiplication method

Lets start with a number 55 again.

Add 5 from the original number: 55+5=60.

We will call this number our base number 1.

Subtract 5 from the original number: 55-5=50

We will call this base 2.

Multiply base 1 to base 2 and add 25: 50x60+25=3025

Wow!  That is really amazing!

Lets try 205²
205-5=200

205+5=210
200X210=42000
42000+25=42025

In later post, I will post how these apply to squares of other numbers.

If you practice and memorize 2 or 3 digit number multiples, you can multiply really fast. I will post some practice on doing these with each unit number digit and you will get really fast and impressive and you will do some difficult problems quickly on standardized tests like the SAT.