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Tutorials - Arithmetic Algebra Arithmetic Geometry Pages: 1 2 3 4 5 SHORTCUT TECHNIQUE TO FIND THE SQUARE OF A NUMBER This technique has only one prerequisite- that you know the squares of numbers between 1 and 25. Not a difficult task at all. At the end of this short tutorial you can find the squares of numbers without even putting your pen to paper!! 1) For Numbers between 25 and 75 2

Eg 29) Calculate 44

STEP 1: Take the difference from 25 (44-25=19). This will be the first two digits=19 _ _ 2

STEP 2: Take the square of the difference from 50 (50-44=6. 6 =36). This will be the last two digits= _ _ 36 2

Thus 44 = 1936 2

Eg 30) Calculate 42

STEP 1: Take the difference from 25 (42-25=17). This will be the first two digits=17 _ _ 2

STEP 2: Take the square of the difference from 50 (50-42=8. 8 =64). This will be the last two digits= _ _ 64 2

Thus 42 = 1764 2

Eg 31) Calculate 38

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STEP 1: Take the difference from 25 (38-25=13). This will be the first two digits=13 _ _ 2

STEP 2: Take the square of the difference from 50 (50-38=12. 12 =144) Note that ”1” will be the carry over 44 will be the last two digits= _ _ 44 2

Thus 38 = 1444 b. For Numbers between 75 and 125 Eg 32) Calculate102

2

STEP 1à Take the difference with respect to 100 (102-100=2) and add it to the number itself= 1022=104. This will be the first three digits=104 _ _ 2

STEP 2à Take the square of the difference from 100 (102-100=2. 2 =04). This will be the last two digits= _ _ _04 2

Thus 102 = 10404 2

Eg 33) Calculate 112

STEP 1: Take the difference with respect to 100 (112-100=12) and add it to the number itself= 112+12= 124. This will be the first three digits=124 _ _ 2

STEP 2: Take the square of the difference from 100 (112-100=12. 12 =144). 1

This will be the last two digits with “1” being a carry over= _ _ _44 2

Thus 112 = 12544 2

Eg 34) Calculate 98

STEP 1: Take the difference with respect to 100 (98-100= -2) and subtract it from the number itself= 98-2= 96. This will be the first two digits=96 _ _ 2

STEP 2: Take the square of the difference from 100 (98-100= -2. (-2) =04). This will be the last two digits= _ _ _04 2

Thus 98 = 9604 The best part is that this technique can be extended for all numbers! You don’t even need to practice this technique once you understand it, and it is so easy that it is almost impossible to forget it!!! Pages: 1 2 3 4 5 Home About Us CAT UPSC Engg/Med CRT Online Course Tablets ©ByjusClasses.com

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