Short Maths Tricks

Let us consider two numbers, 16 and 77 
What would be the solution of 16 x 77?

In this trick, we will begin by picking up the first number. 
16 is an even number, divide it in half and we get, 16/ 2 = 8 
Now, double the second number i.e., 77 x 2 = 154 

For your final answer, you can simply multiply the resultant numbers i.e., 
154x 8 = 1232

Q. Find the answer of 42 x 49

Take the ten’s digit and multiply it by the next highest number, i.e, 4 X 5= 30.
Next, multiply both the one’s digit. 2 x 8 = 16.
Lets put together both the digits and the answer will be 3016. 

To determine whether a number is divisible by 4 or not, we have to analyse its last 2 digits. If they are divisible by 4, the entire number will be divisible by 4. 

For Example: Let us consider 7864, the last 2 digits of this number make the number 64 which is divisible by 4, hence, 7864 is divisible by 4.

Let us consider the number 85
For finding its square, we will begin by squaring the units number which is 5.

We get the answer as 25 and this number will be the last two digits of your answer.
A part of the answer would thus be _  _ 25.

Now, you will have to multiply the ten’s digit number with its very next digit. 
So, 8 x 9= 72.
No 72 becomes your prefix and the final answer is 7225

Let’s take a look at 3364.

Pick up the last two digits first. Here it is 64. 
Since the unit digit is 4, we can say that the unit digit of the square root will either be 2 or 8.

Now, let’s pick up the first two digits. Here it is 33
Since 33 comes between the square of 5 and 6, i.e. 25<33<36, we can say the tens’ digit of the square root of 3364 will be 5. 

So, now we have two options, 52 or 58.
Now to choose between the two, multiply the tens and ones digit of both the options 52 and 58 and compare them with 33 (the thousand and hundred position of the digit).

5*2= 10
5*8=40
The product should be more than or equal to 33.
Since 10<33, the answer has to be 58.
The Square root of 3364 is 58.

Let’s take  39304.

First, pick up the last digit of the cube. Here it is 4. If the last digit is 4, the cube root’s last digit will be 4.

It is important to note in general that:

• If the last digit of a cube root is 8 then the unit digit will be 2.
• If the last digit of a cube root is 2 then the unit digit will be 8.
• If the last digit of a cube root is 3 then the unit digit will be 7.
• If the last digit of a cube root is 7 then the unit digit will be 3.
• If the last digit of a cube root is other than 2, 3, 7 and 8 then put the same number as the unit digit.

Going back to the cube root, we know the unit place for the cube root is 4. Now, ignoring the last three digits of the number, pick up the rest. Here, it is 39.

Check the closest cubes to 39. The closest cube to 39 is 27(Cube of 3) and 64 (cube of 4). Now, since 27 is closer to 39 than 64, the first digit will be 3.

So, the cube root of 39304 will be 34.

Let’s take  x² – 18x + 45 = 0

Multiply the coefficient of x²  with 45. Here it is 1*45=45

Multiply -1 with the coefficient of x. Here it will be -1* (-18)=18

Now, the two values will be on the basis of the digits that add up to become 18 and the same digits when multiplied produce 45.

So, here the answer is 15 and 3. The signs will depend on whether 18 and 45 are positive or not. If both are positive, the answers will be positive, if even one is negative, the answer will be negative.

500 * 200

Multiply 5 and 2
5*2=10

Now, Put all the zeros at the back of 10. Since the numbers had 4 zeros (500 and 200), add 4 more zeros making it 100000

So, 500*200=1,00,000

The basic rule of solving this is subtracting each number with 9 except the last one. This can also be followed for other multiples of 10 like 10,000 or others.

For eg: 572

For this, you need to:

Subtract 5 from 9= 4
Subtract 7 from 9=2

Subtract 2 from 10=8

So, the answer will be 428.

1000-572=428