Suppose you want to find the square of a number which is one less than the number whose square is known, you can use the following method:
Square of 79 will be given as,
(80)^2 - (80 + 79) = 6400 - 159 = 6241.
Finding the square of a number near 50.
Now, if you want to find the square of 51, the formula will be,
(5)^2+1/ (1)^2 = 25 + 1/ 01 = 2601.
This is what you do:
The LHS of the answer is given as (5)^2 + 1 and the RHS is given as the square of the difference of the number from 50.
The RHS of the answer should always contain 2 digits.
Square of a number having all digits 1.
Suppose you want to find the square of 11111,
Check the number of 1s in the number, i.e. 5.
So write 12345 and then write in the reverse order, 4321.
So the answer is 123454321.
Square of a number having all digits 3.
If you want to find the square of 3333
Check the number of 3s in the figure, i.e. 4.
So write three 1s, one 0, three 8s and one 9.
Three because the number of 1s and 8s must be one less than the number of 3s in the original number.
The number of 0s and 9s will always be one.
So the answer will be 11108889.
Square of a number having all digits 6.
Suppose you want to find the square of 6,66,666.
See the number of 6s in the value, i.e. 6.
So write five 4s, one 3, five 5s and one 6.
Five because the number of 4s and 5s should be one less than the number of 6s in the value.
The number of 3s and 6s must always be 1.
The answer will be 444443555556.
Square of number having all digits 9.
Finding the square of 9999.
Count the number of 9s in the value, i.e. 4.
So write three 9s, one 8, three 0s and one 1.
Three because the number of 9s and 0s will be one less than the number of 9s in the original number.
The number of 8s and 1s will always be one.
So the answer will be 99980001.
Finding the square of a number ending with 5.
Suppose you want to find the square of 35, the steps will be as follows:
Write the square of 5 (25) as the RHS of the answer.
Now multiply 3 with its consecutive number, i.e. 4 (3 x 4 = 12) and write as the LHS.
So the answer will be 1225.
Multiplying two numbers which have the same number in the ten's place and the numbers in the unit place add up to 10.
Finding the product of 64 and 66.
First, find the product of the numbers in the unit's place. Here, it will be 4 x 6 = 24. This will be the RHS of the answer.
Second, multiply the number in the ten's place with its consecutive number.
Therefore, 6 x 7 = 42. This will be the LHS of the answer.
So the answer will be 4224.
Finding the cube root of a number.
For finding the cube root of any number, first put a comma after 3 digits from right.
e.g. Finding the cube root of 9261.
Put a comma after three digits from right. i.e. 9,261.
Now check the last digit of the number, here 1. And put the number whose cube has the last digit as the last digit of the number whose cube root is to be found. This will be the RHS of the answer.
Now, check the number on the left of the comma.
Check which number has its cube less than the number left of the comma. Over here, it will be 2 as cube of 2 = 8 and 8 is less than 9 and the cube of 3 will be more than 9. This will be the LHS of the answer.
So the answer will be 21.