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Comment on Squaring Numbers Ending in 5
Does this work if the base is
Yes. Keep in mind that x² = (
Yes. Keep in mind that x² = (-x)².
For example, 3² = 9, and (-3)² = 9.
Likewise, 35² = (-35)² = 1225, and 65² = (-65)² = 4225
Sir, How can we Find Last 2
The last (units) digit is
The last (units) digit is pretty straightforward, but in most cases, the last 2 digits is outside the scope of the GMAT.
Does this technique is also
Good question.
Good question.
The answer is no; the technique can't be extended to powers other than 2.
I think this technique can
That's correct; the technique
That's correct; the technique works on for numbers ending in 5 (thus the title :-)
Majestic!
Indeed :-)
Indeed :-)
Amazing!
Hi Brent,
Are there more techniques like this , which can help us to save time on gmat?
There are tons of time-saving
There are tons of time-saving techniques sprinkled throughout the course.
May I ask why?
Why does the technique work?
Once I know it, it should remind me
Here's why the technique
Here's why the technique works:
First recognize that any integer with units digit 5 can be expressed in the form 10k + 5
Some examples: 35 = (10)(3) + 5, 85 = (10)(8) + 5, 115 = (10)(11) + 5
So, squaring an integer with units digit 5 is the same as squaring 10k + 5.
Now let's see what happens when we square 10k + 5.
(10k + 5)² = 100k² + 100k + 25
= (100)(k)(k + 1) + 25
As we can see, (k)(k + 1) represents the product of the value that comes before units digit 5 and 1 greater than that value (just like in the video)
We then multiply that product by 100, and add 25 to the end (just like in the video).
Does that help?