Math hacks you might not know.

       Math hacks

As I have said earlier this blog is not only to provoke technology but we will also share daily life tips that can really help you.

In this hectic world sometimes all we just need is a shortcut. An easy way out , nobody wants to wait for anything and if somebody is willing to tell you some sort of secret to make it easier for you than you could just subscribe his blog. Just kidding.

Everybody has their own way of solving maths and they apply their own perspective no matter what the teacher told them to do. If  they'd understood it. They would make a shortcut out of it.

So I'm gonna tell you a basic math tricks that nobody has ever told you before.

I'm gonna show you how to get square root of any number within seconds. 

                                          Working With Square Roots:

1. Know what range square root is in , Since squaring numbers ending with 0 and squaring numbers ending with 5 are both easy, we can get the answer within the range of 5.
2. If the number is a perfect square , then we can know what the ending digit of the answer will be by just looking at the ending digit of the question.

Whenever we take a square of 1 it always ends with 1

Whenever we take a square of 2 it always ends with 4

Whenever we take a square of 3 it always ends with 9

Let's see it more clearly

1² = 1   11² = 121 21² = 441 31² = 961  41² = 1681

2² = 4   12² = 144 22² = 484 32² = 1024 42² = 1764

3² = 9   13² = 169 23² = 529 33² = 1089 43² = 1849

If the number ends in a:

1 -> then the ending digit is 1 or 9.

4 -> then the ending digit is 2 or 8.

5 -> then the ending digit is 5.

6 -> then the ending digit is 4 or 6.

9 ->  then the ending digit is 3 or 7.

This way we can say that if a number is ending with numbers (2 , 3, 7, 8) then they are not perfect square.

Now I’m gonna show you some examples.

Example No. 1:  √ 5329 will be _____.

• We know the last number must be 3 or 7.

• Now we chop off last two digits and we focus on remaining numbers i.e. 53.

• We know that 7²=49 and 8²=64, since 53 are in between these two numbers, our answer is between 70 and 80.

• Now, we know that the first digit of our answer is ‘7’. We simply multiply it by its next higher digit which is 7x8=56.

• Since 53 is less 56, therefore the answer will be the lower of the two digits i.e. 3.

• The answer is 73. 

Example No. 2: √ 15876 will be _____.

• We know the last number must be 4 or 6.

• Now we chop off last two digits and we focus on remaining numbers i.e. 158.

• We know that 12²=144 and 13²=169, since 158 are in between these two numbers, our answer is between 120 and 130.

• Now, we know that the first two digits of our answer are ‘12’. We simply multiply it by its next higher digit which is 12x13=156.

• Since 158 is greater  than 156, therefore the answer will be the greater of the two digits i.e. 6.

• The answer is 126.

                             Working with Cube Roots:

Working with cube roots is very similar to working with square roots.

1. By looking at the last number, we can determine the last digit of the answer. If the last digit ends in:
   
   1 -> then the ending digit is  1.
   
   8 -> then the ending digit is  2.
   7 -> then the ending digit is  3.
   4 -> then the ending digit is  4.
   5 -> then the ending digit is  5.
   6 -> then the ending digit is  6.
   3 -> then the ending digit is  7.
   2 -> then the ending digit is  8.
   9 -> then the ending digit is  9.  
   
2. Once the last digit is determined, write it down and mentally chop off the last 3 digits under the cube root.
3. Now, using your knowledge of cubes, find what numbers the remaining are between. Write the smallest of these numbers.

Example No. 1: Cube root of 373248 will be _____.

• We know the last digit ends in a 2. Write 2.

• Chopping off last 3 digits, we are left with 373.

• We know that 7³=343 and 8³=512, so the first digit is 7.

• The answer is 72.

Example No. 2: Cube root of 1601613 will be _____.

• We know the last digit ends in a 7. Write 7.

• Chopping off last 3 digits, we are left with 1601.

• We know that 11³=1331 and 12³=1728, so the first digit is 11.

• The answer is 117.

                           WORKING WITH MULTIPLICATION:

Multiply by 11 :

(Case No.1)

  72x11 = _____

  Add the two numbers and place the result in middle.

Example:

7 (7+2) 2 x 11 = 792

(Case No.2)

99x11 = _____

Add the two numbers and place result in middle:

9 (18) 9

Now use the second number for the middle number and add the first number to the other first number.

i.e.

(9+1)(8)9 = 99x11=1089

Multiply by 12 :

To multiply any number by 12 just double the last digit and thereafter double each digit and add it to its neighbour.

Let’s take a look at an example.

We have 21314x12 = ______

We will always write it as ‘021314’.

Step 1: 021314 x 12 = _____8 (double of Last Digit 4=8)

Step 2: 021314 x12 = ____68 (now double of 1=2 and add it to neighbor i.e. 4, 2+4=6)

Step 3: 021314 x12 = ___768 (now double of 3=6 and add it to neighbor i.e. 1, 6+1=7)

Step 4: 021314 x12 = __5768 (now double of 1=2 and add it to neighbor i.e. 3, 2+3=5)

Step 5: 021314 x12 = _557668 (now double of 2=4 and add it to neighbor i.e. 1, 4+1=5)

Step 6: 021314 x12 = 255768 (now double of 0=0 and add it to neighbor i.e. 2, 0+2=2)

The answer is ‘255768’

                        Checking the Divisibility:

Dividing By 2:

A number is divisible by 2 if the last digit is even. The remainder in the case of 2 will always be one if the last digit is odd.

Dividing By 3:

A number is divisible by 3 if the sum of all digits is divisible by 3.

Example: 34,164 is divisible by 3 because 3+4+1+6+4=18 which is divisible by 3.

To find the remainder of a number divided by 3, add the digits and find that remainder. So if the digits added together equals 13 then the number has a remainder of 1 since 13 divided by 3 has a remainder of 1.

Dividing By 4:

A number is divisible by 4 if the last 2 digits are divisible by 4.

Example: 34,164 is divisible by 4 because 64 is divisible by 4.
To find the remainder of a number divided by 4. Take the remainder of the last 2 digits. So if the last two digits are 13 then the remainder is 1, since 13 divided by 4 has a remainder of 1.

Dividing By 5:

A number is divisible by 5 if the last digit is 5 or 0.

To find the remainder of a number divided by 5, simply use the last digit. If it is greater than 5, subtract 5 for the remainder.

Dividing By 6:

A number is divisible by 6 if it is divisible by 2 and 3 both.

Example: 34,164 is divisible by 6 because it is divisible by 2 and 3 both.

Dividing By 7:

A number is divisible by 7 if the following are true:

1. Multiply the ones digit by 2.
2. Subtract this value from rest of the number.
3. Continue this pattern until you find a number you know is or is not divisible by 7.

Example 1:  7203 is divisible by 7 because:

• 2x3 = 6.
• 720-6 = 714, which is divisible by 7.

Example 2: 14443 is not divisible by 7 because:

• 3x2 = 6
• 1444-6 = 1438
• 8x2 = 16
• 143-16 = 127 this is not divisible by 7.

Note: This method takes a lot of practice and is sometimes easier to just work it out individually.

Dividing By 8:

A number is divisible by 8 if the last 3 digits are divisible by 8.

Example: 34,168 is divisible by 8 because 168 is divisible by 8.

To find the remainder of a number divided by 8 take the remainder of the last 3 digits. So if the last 3 digits are 013 then the number has a remainder of 5.

Dividing By 9:

A number is divisible by 9 if the sum of all digits is divisible by 9.

Example: 34,164 is divisible by 9 because 3+4+1+6+4=18 which is divisible by 9.

To find the remainder of a number divided by 9, add the digits and find that remainder. So if the digits added together equal 13 then the number has a remainder of 4 since 13 divided by 9 has a remainder of 4.

Dividing By 10:

A number is divisible by 10 if the last digit is a 0.
To find the remainder of a number divisible by 10 simply use the last digit.

Dividing By 11:

A number is divisible by 11 if these are true:

1. Starting from the one’s digit, add every other digit.
2. Add the remaining digits together.
3. Subtract 1^st step from the 2^nd step.

If this value is zero, then the number is divisible by 11. If not zero then this is the remainder after dividing by 11 if it is positive. If the number is negative, simply add 11 to get the remainder.

Example: 6613585 is divisible by 11 since (5+5+1+6) – (8+3+6) = 0.

Dividing By 12:

A number is divisible by 12 if it is divisible by 3 and by 4.

Example: 34,164 is divisible by 12 because it is divisible by 3 and 4 both.