In this page on Speed Math, we have presented few topics accommodating few speed and short methods to work out mathematical problems. Few examples have been given for the students to understand these methods in a better manner. The students are advised to practise these methods before start following them regularly.


Method : 1 >>> Square of a number by binomial Theorem :


The binomial theorem is : (a + b)² = a² + 2ab + b²


(a + b)² = |a|b| x |a|b| = |a²|2ab| b²


Example : 1


To calculate 36²


(a + b)² = |a|b| x |a|b| = |a²|2ab| b²


Here, a = 3 and b = 6


36² = |3|6| x |3|6|


= |3|6| x |3|6|


= |3²|2 x 3 x 6| 6²|


= |9|36|36|


Let us work from the last digit.


In the 36, retain the digit 6 and carry over the 3 to the next 36.


36 + 3 = 39


In this 39, retain the 9 and carry over the 3 to the next number 9.


9 + 3 = 12


Now the answer is 12-9-6 = 1296


36² = 1296


Example : 2


To calculate 5641²


(a + b)² = |a|b| x |a|b| = |a²|2ab| b²


Here, a = 56 and b = 41


5641² = |56|41| x |56|41|


= |56|41| x |56|41|


= |56²|2 x 56 x 41| 41²|


= |3136|4592|1681|


Let us work from the last digit.


Since both (a and b) are 2-digit numbers, the last 2 digits are retained.


In the 1681, retain the digits 81 and carry over the 16 to the next 4592.


4592 + 16 = 4608


In this 4608, retain the 08 and carry over the 46 to the next number 3136.


3136 + 46 = 3182


Now the answer is 3182-08-81 = 31820881


5641² = 31820881


Method : 2 >>> To find out the cube root of a number :


To find out the cube root of the number 474552, the number being the perfect cube of a number...


Since we have to find out the third root of a number, we have to divide the given number into three digit segments from the right.


474552 becomes |474|552|


Since there are 2 segments, the cube root of this number also will have 2 digits.


Let the 2-digit number be ab.


Now take the first segment |474|.


Now we must find the greatest value of a such that a³ < |474|.


7 x 7 x 7 = 343


8 x 8 x 8 = 512


So, 7 satisfies this condition.


343 < 474


7³ < |474|


So, a = 7


Let us take the second segment |552|.


474552 is said to be a perfect cube.


So, the last digit of |552| ends in 2.


If the last digit of the number ends in 8, the cube of that number will end in 2.


So, b = 8


From these calculations, we can say that that cube root of 474552 is 78.


78³ = 474552







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