The Cube Root Trick


If someone cubed a two-digit number on a calculator and gave you the result - but not the original number - could you extract the cube root? With this trick, you'll be able to do just that - instantly!
A bit of homework is required for this trick, but it's worth the effort if you like to show off.

First, memorize the cubes of the digits 1 through 9:

1, 8, 27, 64, 125, 216, 343, 512, 729.

Next memorize the "endings" of the cubes. For example, the ending of 9^3 is 9, because 9^3 = 729. The "ending" (or last digit) is 9.

So let's make a list. "1 cubed ends in 1" is abbreviated "1 --> 1".

1 --> 1
2 --> 8
3 --> 7
4 --> 4
5 --> 5
6 --> 6
7 --> 3
8 --> 2
9 --> 9

These are easily memorized. 1 and 9 (at the extremes) are "self-enders", as are the 4, 5, and 6 (in the center). The others involve "a sum of 10": 2 ends in 8, 8 ends in 2, 3 ends in 7, and 7 ends in 3.

Now how to do the trick!
Tell a friend to secretly pick any two-digit number and then have him or her use a calculator to cube it. Let's say he picks 76. So using the calculator he computes 76 x 76 x 76 . He then tells you the cube: 438,976.

To instantly determine his original number (ie, compute the cube root), follow these easy steps:
Drop the last three digits and find the largest cube contained in 438. This is 7^3 = 343, so the tens-digit is 7.
(This is why you had to memorize the cubes of the digits 1 through 9)
Now go back to the last three digits. Look at the last digit, 6. That's the same ending as 6^3, so your units-digit is 6.
(This is why you had to memorize the "endings" of the cubes for digits 1 through 9)So the cube root of 438,976 is 76

Another example:
Let's say your friend chooses a secret two-digit number whose cube is 79,507. How do you instantly determine the cube root?
Drop the last three digits and find the largest cube in 79. This is 4^3 = 64, so the tens-digit of the cube root is 4.
Now go back to the last three digits. Look at the last digit, 7. That's the same ending as 3-cubed. So the units-digit of your cube root is 3.Therefore, the cube root of 79,507 is 43.

How to Calculate Square Roots without a Calculator


Ever wonder how to determine the square root of a number without the aid of a calculator? Believe it or not, people used to do this. Here's one method for doing so.
If you're good with long division, here's a quick way to find pretty accurate square roots without the aid of a calculator. Let's try 24.6.
Make a guess. It can be a very bad guess. It doesn't matter. You can even guess 1. Let's try 5 since 5^2 is 25, which is pretty close to 24.6.
Divide 24.6 by 5. 24.6 / 5 = 4.92.
Now, comes the trick: Pick a new guess between 5 and 4.92 and divide it into 24.6 again. Let's try 4.95. 24.6 / 4.95 = 4.96. 4.96 is pretty close to 4.9598 which is the actual square root of 24.6.
Repeat steps 2 and 3 to any desired level of accuracy. The further you go, the harder the long division becomes. But the first few cycles yield a pretty close answer.The reason this works is because n*n = 24.6 and n = 24.6 / n. Therefore, the real square root will always be somewhere between 24.6 / n and n.

Multiply Up to 20 X 20 In Your Head


Got 5 minutes to spare? That's all the time you need to learn how to quickly multiply two numbers from 11 to 19 in your head.

With this trick, you will be able to multiply any two numbers from 11 to 19 in your head quickly, without the use of a calculator.
I will assume that you know your multiplication table reasonably well up to 10x10.

Lets try 15 x 13.

1. Always place the larger number of the two on top in your mind.

2. Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.

3. Now add 15 + 3 = 18

4. Add a zero behind it (i.e., multiply by 10) to get 180.

5. Multiply the covered lower 3 by the single digit above it, in this case the "5" (3 x 5 = 15)

6. Add the products from steps 5 and 6 to get your answer. 180 + 15 = 195.

That's it! Wasn't that easy? Practice it on paper first!

Multiply two 3-digit numbers mentally


The trick I am going to explain is called the cross-multiplication technique... but not the one you know.


Lets start with 123 * 456.

^Step 1--- arrange the numbers in order (one on top of the other) your pick.

123
456
----------

start by first multiplying 6*3=18. write down the 8 and carry the 1 mentally.

123
456
---------- CARRY 1
----8

^Step 2---- attempt to form an invisible X
It may not sound simple at first but I'll explain.

Start by observing the 6 & 2, then the 5 & 3. Make a line between those numbers and you will get an X.

Now multiple 6*2=12 PLUS(+) 5*3=15
so 12 + 15 = 27
27 + 1 (the carry)= 28
Now write down the 8 and carry the 2 mentally.

123
456
---------- CARRY 2
---88


^Step 3--- now examine the numbers 6 & 1, 4 & 3, then in the middle 2 & 5.

Multiply them and add em' all up:
6*1=6 + 4*3=12 + 5*2=10
so 6 + 12 +10 = 28 PLUS carry 2 = 30.

Write down the 0 and carry the 3.

123
456
---------- CARRY 3
--088

^Step 4--- Now we will attempt the invisible X for the last time. This time take notice of the numbers 5 & 1, 4 & 2
multiply them and add em' all up:
5*1=5 + 4*2=8
so 5 + 8 = 13 PLUS carry 3 = 16.
Write down the 6 and carry the 1.

123
456
---------- CARRY 1
--6088

^Step 5 (final step)--- In the beginning we started by multiplying 6 & 3. Now we will multiply 4 & 1.
so 4*1=4 + carry 1 = 5

Write it down and the behold the FINAL ANSWER!

123
456
----------
56088

Nothing in this world is easy to learn at first shot, so give it some time like I did and become a master at the skill. It just might help you in the long run because I myself can multiply any two 3-digit numbers in my head in less than 5 seconds (using the method I just explained) and I'm getting better. Good luck!

aray ko...weakness ko kaya math...tanungin mo na ako ng iba wag lang math...

:thumbsup: sir lance... tinuro sa amin itong mga tricks na ito nung high school pa ako.... kasi blitz ung mga contest kaya kailangan ng mga tricks na ganito... :thanks: for refreshing this tricks to me... hahaha...

hakhak... highschool days... nagbabalik sa akin!!!!