যদি আপনাকে প্রশ্ন করি ১১১১১১ (ছয়টি ১)এর বর্গ কত? ক্যালকুলেটার ছাড়া উত্তর দিতে কতক্ষণ লাগবে? আমি আপনাকে খুবই সহজ একটি উপায় বাতলে দিতে পারি, যার সাহায্যে ক্যালকুলেটার ছাড়াই ঝটপট এর উত্তর বলে দিতে পারবেন।

প্রথমেই গুণে ফেলুন কটি ১ আছে (ছয়টি)।
এবার ১ থেকে ৬ পর্যন্ত লিখুন, এবং সেই ছয় থেকেই আবার উল্টোগুনে ১ পর্যন্ত লিখে ফেলুন।
যেমনঃ ১২৩৪৫৬৫৪৩২১।
এটাই উত্তর।

যদি ১ এর সংখ্যা হয় ৯টি (১১১১১১১১১) তাহলে?
কোনো ব্যাপারই না, ১ থেকে ৯ পর্যন্ত লিখুন, এবং সেই ৯ থেকেই আবার উল্টোগুনে ১ পর্যন্ত লিখে ফেলুন।
যেমনঃ ১২৩৪৫৬৭৮৯৮৭৬৫৪৩২১।
বর্গ করা হয়ে গেলো।

এভাবে দুই থেকে নয়টি পর্যন্ত রিপিট্টে ১ থাকলে ঝটপট তাদের বর্গ নির্ণয় করে ফেলতে পারবেন।

661^2 = 436921
6661^2 = 44368921
66661^2 = 4443688921
666661^2 = 444436888921
6666661^2 = 44444368888921
66666661^2 = 4444443688888921
666666661^2 = 444444436888888921
6666666661^2 = 44444444368888888921
66666666661^2 = 4444444443688888888921

62^2 = 3844
662^2 = 438244
6662^2 = 44382244
66662^2 = 4443822244
666662^2 = 444438222244
6666662^2 = 44444382222244
66666662^2 = 4444443822222244
666666662^2 = 444444438222222244
6666666662^2 = 44444444382222222244
66666666662^2 = 4444444443822222222244

63^2 = 3969
663^2 = 439569
6663^2 = 44395569
66663^2 = 4443955569
666663^2 = 444439555569
6666663^2 = 44444395555569
66666663^2 = 4444443955555569
666666663^2 = 444444439555555569
6666666663^2 = 44444444395555555569
66666666663^2 = 4444444443955555555569

64^2 = 4096
664^2 = 440896
6664^2 = 44408896
66664^2 = 4444088896
666664^2 = 444440888896
6666664^2 = 44444408888896
66666664^2 = 4444444088888896
666666664^2 = 444444440888888896
6666666664^2 = 44444444408888888896
66666666664^2 = 4444444444088888888896

65^2 = 4225
665^2 = 442225
6665^2 = 44422225
66665^2 = 4444222225
666665^2 = 444442222225
6666665^2 = 44444422222225
66666665^2 = 4444444222222225
666666665^2 = 444444442222222225
6666666665^2 = 44444444422222222225
66666666665^2 = 4444444444222222222225

66^2 = 4356
666^2 = 443556
6666^2 = 44435556
66666^2 = 4444355556
666666^2 = 444443555556
6666666^2 = 44444435555556
66666666^2 = 4444444355555556
666666666^2 = 444444443555555556
6666666666^2 = 44444444435555555556
66666666666^2 = 4444444444355555555556

672 = 4489
667^2 = 444889
6667^2 = 44448889
66667^2 = 4444488889
666667^2 = 444444888889
6666667^2 = 44444448888889
66666667^2 = 4444444488888889
666666667^2 = 444444444888888889
6666666667^2 = 44444444448888888889
66666666667^2 = 4444444444488888888889

68^2 = 4624
668^2 = 446224
6668^2 = 44462224
66668^2 = 4444622224
666668^2 = 444446222224
6666668^2 = 44444462222224
66666668^2 = 4444444622222224
666666668^2 = 444444446222222224
6666666668^2 = 44444444462222222224
66666666668^2 = 4444444444622222222224

669^2 = 4761
669^2 = 447561
6669^2 = 44475561
66669^2 = 4444755561
666669^2 = 444447555561
6666669^2 = 44444475555561
66666669^2 = 4444444755555561
666666669^2 = 444444447555555561
6666666669^2 = 44444444475555555561
66666666669^2 = 4444444444755555555561

6610^2 = 43692100
66610^2 = 4436892100
666610^2 = 444368892100
6666610^2 = 44443688892100
66666610^2 = 4444436888892100
666666610^2 = 444444368888892100
6666666610^2 = 44444443688888892100
66666666610^2 = 4444444436888888892100
666666666610^2 = 444444444368888888892100

6612^2 = 43718544
66612^2 = 4437158544
666612^2 = 444371558544
6666612^2 = 44443715558544
66666612^2 = 4444437155558544
666666612^2 = 444444371555558544
6666666612^2 = 44444443715555558544
66666666612^2 = 4444444437155555558544
666666666612^2 = 444444444371555555558544

620^2 = 384400
6620^2 = 43824400
66620^2 = 4438224400
666620^2 = 444382224400
6666620^2 = 44443822224400
66666620^2 = 4444438222224400
666666620^2 = 444444382222224400
6666666620^2 = 44444443822222224400
66666666620^2 = 4444444438222222224400
666666666620^2 = 444444444382222222224400

91^2 = 8281
991^2 = 982081
9991^2 = 99820081
99991^2 = 9998200081
999991^2 = 999982000081
9999991^2 = 99999820000081
99999991^2 = 9999998200000081
999999991^2 = 999999982000000081
9999999991^2 = 99999999820000000081
99999999991^2 = 9999999998200000000081

92^2 = 8464
992^2 = 984064
9992^2 = 99840064
99992^2 = 9998400064
999992^2 = 999984000064
9999992^2 = 99999840000064
99999992^2 = 9999998400000064
999999992^2 = 999999984000000064
9999999992^2 = 99999999840000000064
99999999992^2 = 9999999998400000000064

93^2 = 8649
993^2 = 986049
9993^2 = 99860049
99993^2 = 9998600049
999993^2 = 999986000049
9999993^2 = 99999860000049
99999993^2 = 9999998600000049
999999993^2 = 999999986000000049
9999999993^2 = 99999999860000000049
99999999993^2 = 9999999998600000000049

94^2 = 8836
994^2 = 988036
9994^2 = 99880036
99994^2 = 9998800036
999994^2 = 999988000036
9999994^2 = 99999880000036
99999994^2 = 9999998800000036
999999994^2 = 999999988000000036
9999999994^2 = 99999999880000000036
99999999994^2 = 9999999998800000000036

95^2 = 9025
995^2 = 990025
9995^2 = 99900025
99995^2 = 9999000025
999995^2 = 999990000025
9999995^2 = 99999900000025
99999995^2 = 9999999000000025
999999995^2 = 999999990000000025
9999999995^2 = 99999999900000000025
99999999995^2 = 9999999999000000000025

96^2 = 9216
996^2 = 992016
9996^2 = 99920016
99996^2 = 9999200016
999996^2 = 999992000016
9999996^2 = 99999920000016
99999996^2 = 9999999200000016
999999996^2 = 999999992000000016
9999999996^2 = 99999999920000000016

97^2 = 9409
997^2 = 994009
9997^2 = 99940009
99997^2 = 9999400009
999997^2 = 999994000009
9999997^2 = 99999940000009
99999997^2 = 9999999400000009
999999997^2 = 999999994000000009
9999999997^2 = 99999999940000000009
99999999997^2 = 9999999999400000000009

98^2 = 9604
998^2 = 996004
9998^2 = 99960004
99998^2 = 9999600004
999998^2 = 999996000004
9999998^2 = 99999960000004
99999998^2 = 9999999600000004
999999998^2 = 999999996000000004
9999999998^2 = 99999999960000000004
99999999998^2 = 9999999999600000000004

99^2 = 9801
999^2 = 998001
9999^2 = 99980001
99999^2 = 9999800001
999999^2 = 999998000001
9999999^2 = 99999980000001
99999999^2 = 9999999800000001
999999999^2 = 999999998000000001
9999999999^2 = 99999999980000000001
99999999999^2 = 9999999999800000000001

9910^2 = 98208100
99910^2 = 992008100
999910^2 = 99920008100
9999910^2 = 9999200008100
99999910^2 = 999992000008100
999999910^2 = 99999920000008100
9999999910^2 = 9999999200000008100
99999999910^2 = 9999999982000000008100
999999999910^2 = 999999999820000000008100

9912^2 = 98247744
99912^2 = 9982407744
999912^2 = 999824007744
9999912^2 = 99998240007744
99999912^2 = 9999982400007744
999999912^2 999999824000007744
9999999912^2 = 99999998240000007744
99999999912^2 = 9999999982400000007744
999999999912^2 = 99999999824000000007744

9920^2 = 98406400
99920^2 = 9984006400
999920^2 = 999840006400
9999920^2 = 999840006400
99999920^2 = 99998400006400
999999920^2 = 9999984000006400
9999999920^2 = 999999840000006400
99999999920^2 = 99999998400000006400
999999999920^2 = 999999999840000000006400
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