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Mental Root Square Calculation.

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Last edited: 2020-07-01. YMD

Mental arithmetic: Calculate square roots by heart.

In the series of articles on improving your memory, this time I am going to talk about calculating the square root of the square of a random number between 1 and 100.

You can learn this calculation trick fairly quickly and you can use it among your friends
(if you have one) or use it at a family celebration to demonstrate that you have a high IQ.

I work here with numbers of which the result of the square root is an integer. So no decimal places.

What is the formula of square root?

If X=9 then what is the square root of X. And how do I calculate this mentally? What is the square root anyway.

Well, you can take this quite literally. If you draw a square on squares-paper. And you make this so big that the square consists of 9 squares. Then you SEE that the base or 1 side is 3 diamonds. So this 3 is the root. And so, you have to wonder which number do I have to multiply by myself to get the requested X.

Thus, it’s the opposite of the square of a number. Hence the name ‘square root’ because you are looking for the root number. Which you have to square to calculate the area of the square as a result.

Cubic root = power 3 derivation.

The same is for a cubic shape. But this has 3 dimension shape. So a 10inch by 10 by 10 cube, has 1000 inch³ volume. In metrics this is much more logical. Ex. 1 centimeter cube = 1cc volume. And 10 by 10 by 10cm = 1000 cubic cm = 1000mili liter = 1 liter. More evolved country’s use the logical metric system with real measurements. (not inch, gallon, feet,…)

How to calculate square root mentally?

So if you don’t have or want to use a calculator. Then is is like normal multiplications. You have to LEARN the basic values by heart.

squared values you have to know:

  • 1 squared = 1
  • 2 squared = 4
  • 3 squared = 9
  • 4 squared = 16
  • 5 squared = 25
  • 6 squared = 36
  • 7 squared = 49
  • 8 squared = 64
  • 9 squared = 81
  • 10 squared = 100

And how with bigger numbers? Well that will be explained in this mental power mind trick 😎

Mental Root Square Calculation – How?

Step 1 – Have your counter-party say a number between 1 and 10,000 of which you will calculate the square root by heart.

Now how do you know if the outcome will be an integer?
Give them a calculator and tell them to multiply a random number between 1 and 100 with themselves and tell you the outcome. And you then give them the square root of that number as an answer.

Step 2 – Calculate the square root by heart.

To do this, you must first memorize the following set of squares.

10 squared = 100
15 squared = 225
20 squared = 400
25 squared = 625
30 squared = 900
35 squared = 1225
40 squared = 1600
45 squared = 2025
50 squared = 2500
55 squared = 3025
60 squared = 3600
65 squared = 4225
70 squared = 4900
75 squared = 5625
80 squared = 6400
85 squared = 7225
90 squared = 8100
95 squared = 9025
100 squared = 10000

And further this table

Last figure result
<5> 5last digit
statement
191
284
466
379

Now that you have learned all this by heart, you should normally be able to answer the question of what is the square root of X within the second.
(where X is the square of a number from 1 to 100)

square root example:

What is the root of 1444?
The only thing you have to do is see which of the outcomes you have learned by heart.
In this case, therefore, between 1225 and 1600. And so you know that the outcome must be between 35 and 40.
The table serves this purpose. 1444 ends in a 4 so your outcome must end in 2 or 8
Since it must be greater than 35, it is therefore 38.
38 × 38 = 1444

Another square root example.

Exercise = 6724
This is between 6400 and 7225. The result is therefore between 80 and 85
The statement ends in 4. So again 2 or 8 according to the table but the last digit must be less than 5 (result less than 85) so the result is 82.


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