Short Tricks For Squares Cubes And Multiplication

Short Tricks for Squares, Cubes and Multiplication

Shortcut tricks for squares, cubes and multiplication are very important for any competitive exam. Candidates aspiring to appear for competitive exams under bank like IBPS PO, SBI PO etc will require these shortcut tricks in the quantitative aptitude section. If candidates manage their time then they can do well in the exam.

These tricks are required most while solving problems on simplification. And as simplification is an important part of quantitative aptitude candidates should be fully aware about the shortcut tricks for cubes, squares, square roots, cube roots and multiplication.

Tricks for calculating Square

Type 1: For numbers between 80 to 100 assume that the base is 100. Since there are two zeros in the base, up to two digits will be added.

Example: Find the square of 97.

Here the base is 100

Step 1: First calculate the difference between the base and the number.

100-97 = 3

Step 2: Then subtract the difference from the number

97-3 = 94

Step 3: Now calculate Square of the difference.

\(3^{2}\) = 09

Now the answer will be 9409

Type 2: For numbers between 100 to 120. Here we assume the base is 100.

Example: Find the square of 107.

Step 1: First find the difference between base and the number.

107-100 = 7

Step 2:  Add the difference with the number

107+7 = 114

Step 3: Find the square of the difference

\(7^{2}\) = 49

Now the answer will be 11449

Type 3: For numbers between 50 to 70. Here we assume the base is 50.

Direction: 25 + extra from the base _ square of extra value.

Example:

Square of 51 = 25+1 _ (12) = 26_01 = 2601

Square of 59 = 25+9 _ (92) = 34_81 = 3481

Square of 62 = 25+12_ (122) = 37_144 (Answer is incorrect)

Here 1 should be transferred from 144 to 37 so it will become 38

So, 622 = (37+1)_44 = 3844

682 = 25+18_(182) = 43_324 = (43+3)_24 = 4624

Similarly transferring 3 from 324 to 43, we will get 46 and answer will be 4624

Type 4: For numbers between 30 to 50. Here we assume the base is 50.

Direction: 25 – less from the base _ square of less value

Example:

Square of 46 = 25 – 4 _ 16 = 2116

Square of 49 = 25 – 1 _ (01) = 2401

Square of 43 = 25 – 7 _ (49) = 1849

Square of 34 = 25 – 16 _(256) = 9256 (Answer is incorrect)

Here 2 should be transferred from 256 to 9, we will get 11

And answer will be 1156

Type 5: For numbers between 71 to 79.

Square of numbers between 71 and 79 can be done using both 50-method and 100-method.

Example:

732 = (25+23)_232 = 48_529 = 5329

792 = (79-21)_212 = 58_441 = 6241

Tricks for calculating Cube

Calculating cube of a number consumes a lot of time while solving the quantitative aptitude section of any bank exam. Here are some steps of shortcut tricks on how to calculate cube of a number.

Step 1: Note the cube of tens place digit in a row of four figures. The other 3 numbers in the row of the answer must be written in a geometrical ratio and in the exact proportion which is there between the digits of a number.

Step 2: Write down the 2 times of second and third number just below the second and third number in the next row.

Step 3: Now the 2 rows should be added.

Example:

Find the cube of 13

Step 1:  Note down the cube of the tens place that is 1. And also the geometric ratio between 1 and 3 is 1:3. Therefore the first row is   1   3   9   27

Step 2: Note down the 2 times of second and third number that is 6 and 18.

Step 3: Now adding the rows will give the answer

Therefore by adding the rows we get that the cube of 13 is 2197.

Tricks for Multiplication

Multiplication of numbers having 5 at their unit places

Type 1: When numbers are same.

65×65 = (6×7)_25 = 4225 (Fix 25 in last, multiply 6 from 7 that is 42)

85×85 = (8×9)_25 = 7225 (Fix 25 in last, multiply 8 from 9 that is 72)

115×115 = (11×12)_25 = 13225 (Fix 25 in last, multiply 11 from 12 that is 132)

Type 2: When numbers have difference of 10

65×75 = (6×8)_75 = 4875 (Fix 75 in last, multiply 6 from 8 that is 48)

85×95 = (8× 10)_75 = 8075 (Fix 75 in last, multiply 8 from 10 that is. 80)

115×125 = (11×13)_75 = 14375 (Fix 75 in last, multiply 11 from 13 that is 143)

Type 3: When numbers have difference of 20

65×85 = (6×9)_125 = 54_125 (Fix 125 in the last and multiply 6 from 9 that is 54)

Note: In this 1 from 125 has to be transferred to 55. So, answer will be 5525.

85×105 = (8×11)_125 = 88_125 = 8925

115×135 = (11×14)_125 = 154_125 = 15525

Type 4: When numbers have difference of 30

65×95 = (6×10)_175 = (Fix 175 in the last and multiply 6 from 10 that is 60)

In this 1 from 175 has to be transferred to 60. So answer will be 6175

85×115 = (8×12)_175 = 96_175 = 9775

Multiplication of different numbers

Type 1: When the difference of two numbers is even.

Multiplication = (Middle number)2 – (difference/2)2

19×21 = 202 – (2/2)2 = 400-1 = 399

47×53 = 502 – (6/2)2 = 2500-9 = 2491

73×77 = 752 – (4/2)2 = 5625-4 = 5621

Type 2: Consecutive Number Multiplication:

Square of Small number + small number

12×13 = 122+12 = 144+12 = 156

48×49 = 482+48 = 2304+48 = 2352

How this formula has been derived:

12×13 = 12×(12+1)= 12× 12+12 = 122+12

Type 3: Different numbers (less than 100)

103×108

 +8     +3 and (8×3) = 24

(103+8)_ (+3)×(+8) = 11124 or (108+3)_8×3 = 11124

109×117

 +17   +9

(109+17)_(+9)×(+17) = 126_153 = 12753

Type 4: Different Numbers (less than 100)

96×91

-9   -4

(96-9)_(-9)×(-4) = 8736 or (91-4)_9×4 = 8736

92×87

-13  -8

(92-13)_(-13)×(-8) = 79_104 = 8004

Type 5: Different Numbers (<100>)

103×96

-4     +3

(103-4)_(-4×3) = 99_ (-12) = 9900-12= 9888

Or (96+3)_(-4×3) = 99_-12 = 9900-12 = 9888

These shortcut tricks can help candidates during the exam to save their time. For the upcoming bank exams candidates must be fully prepared of all the strategies that will help them to score good marks in the exam.

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