photo

 

https://upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Compass_Rose_en.svg/512px-Compass_Rose_en.svg.png https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjl220k9qOjAK6ZSUNryH4Xx59hcAuOCP9aXNbGs9FWWxIaLPLjgjNSRUmFstuhyCMYkJ5SCGehlyFp_0gSQn35B8ye5V1ZyCg9fzi_i5iuckYYt12HhsnNhCSRYaBmLSdtxnXdSDwTS14Wir8Y5mGmoHpIELl65Fu7LGNk20mKZyJ7ZAAKCX-RP4Af-Bc/s16000/Slide1.JPG https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR4u2oO9rC5vkxQMstklAfPeRn77DFFrqJJ9x-33Z5dLcluT6-JjxVyr3pR0P5lB7Mrt_yev6OPI2YmDkFNyGx6JGsoKBr7krtGgguAfv5KGW-R0Cd9ef-bVkaSYjAJJsYyjXjwUHnfAqm672Ky9XiZxtZnRUPEPCt7ZtKlWZmH-i4CvxL5e6cGnx4Mio/s16000/Slide2.JPG

 Vedic Maths

FUN WITH MATHEMATICS
squaring numbers

Vedic Mathematics- Squaring a Number

Yavadunam

– Whatever the deficiency subtract that deficit and write alongside the square of

– Squaring numbers close to a base

Ekadhikena Purvena 

– Squaring numbers ending in 5

DwandaYoga

– Duplex Combination Process 

VEDIC MATHEMATICS -  SUB-SUTRA  

3. Yavadunam Tavadunikrtya Varganca Yojayet

– Whatever the deficiency subtract that deficit and write alongside the square of

EXAMPLE 1. 

Square of 8

10 – 8 = 2,  square of 2 is 4

8 – 2 = 6

Thus, Square of 8 = 64

EXAMPLE 2. 

Square of 6

10 – 6 = 4,  square of 4 is 16

6 – 4 = 2

Thus, Square of 6 = 2(1)6=36

RULE:

To find squares of numbers close to base 10,

 we subtract the number from base 10 and take a square of the result. 

Then we subtract the result from the number and cross the results.

VEDIC MATHEMATICS -  SUB-SUTRA 

3. Yavadunam Tavadunikrtya Varganca Yojayet

– Squaring numbers close to a base

Examples:  96² 

 = 92/16 { LHS 96 is 4 less than 100. so reduce it by 4  (96 – 4 = 92) 

lessen 96 still further by same number

{ RHS square the deficiency (4 x 4 = 16)

103²  

= 106/09 { LHS 100 + 3 increase by 3  / / 103 + 03 = 106

 { RHS square the increment 03 x 03 = 09)

1011²  

 = 1022/121 { LHS 1000+11=1022 / RHS square the increment (11 x 11 = 121)

VEDIC MATHEMATICS -  SUB-SUTRA 

3. Yavadunam Tavadunikrtya Varganca Yojayet

– Squaring numbers close to a base

Examples:

991²  

 = 982/081 { LHS 991-9/ RHS 009 x 009 }

93²  

 = 86/49 { LHS 93-7/ RHS 07 x 07 }

88²  

 = 76/144 { LHS 88-12/ RHS 12 x 12 }

 = 77/44

VEDIC MATHEMATICS -  SUB-SUTRA 

Ekadhikena Purvena 

– Squaring numbers ending in 5

Examples:  

35² 

  = 3 x (3+1) / 5 x 5

= 3x4 /25

= 1225

85² 

  = 8 x (8+1) / 5 x 5

= 8x9 / 25

= 7225

850² 

  = 8 x (8+1) / 50 x 50

= 8x9 / 2500

= 722500

VEDIC MATHEMATICS -  SUB-SUTRA  

Dvanda Yoga 

– Duplex Combination Process 

Duplex is denoted by D. 

D(3) = 3² = 9

D(43) = 2x4x3 = 24

D(567) = 2x5x7 + 62 = 70 + 36 = 106

D(3456) = 2x3x6 + 2x4x5 = 36 + 40 = 76

D(34567) = 2x3x7 + 2x4x6 + 52 = 42 + 48 + 25 = 115

It goes on….

SQUARE OF 1221 = 1490841

L  R & similar to urdhva tiryagbhyam sutra

Calculate

D(1st digit) -----(1) = 1 x 1 = 1

D( 1st 2 digits)----(12) = 2 x 1 x 2 = 4

D(1st 3 digits)----(122) = 2 x 1 x 2 + 2 x 2 = 4+4=8

D ( All 4 digits)---(1221) = 2 x 1 x 1+2 x 2 x 2=2 + 8=10

D(Last 3 digits)---(221) = 2 x 1 x 2 + 2 x 2 = 4+4=8

D(last 2 digits)---(21) = 2 x 1 x 2 = 4

D(last digit) -----(1) = 1 x 1 =1

Add the carry forward

Answer is 1490841

Vedic Mathematics 

Squaring a 2 digit Number beginning with 1 

Example 1:  

17² 

= 17 x 17

= 1x1 / 2x 7 / 7 x 7 

= 1 / 14 / 49

= 1 / 14 +4 / 9

= 1+1 / 8 / 9

= 289

18² 

= 18 x 18

= 1x1 / 2x 8 / 8 x 8 

= 1 / 16 / 64

= 1 / 16 +6 / 4

= 1+2 / 22 / 4

= 324

Play & Learn with your Friends Kutties! 👍

All the best! 

Thank You🙏🏻

{ title: "Dwanda Yoga", subtitle: "Duplex Combination", desc: "Duplex (D): D(ab)=2×a×b, D(abc)=2×a×c + b².
D(43)=2×4×3=24
D(567)=2×5×7+6²=106
Square of 1221 = 1490841 (using symmetrical duplex).", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcgfeAiyVAQW2XX0PdAqUoXaLb_c9a-IZypPAEc3xadHl4zPaRAtScX7ZNj0cEw3fZS9IhUw6F7XZHZxo4eZgFvpSyXCJT05uikXl3R7LMDoSm8hLFVfm9sK8WiSnQbHqkFnQKtIdij9oFYKsPL_d4yOwbnqYkEF2dHe6U5fesXJhBg7HjiY8xOHo5Oec/s16000/Slide3.JPG" }, { title: "Yavadunam Example 1", subtitle: "Square of 8", desc: "Base 10 → deficiency 2 → 8-2=6, 2²=4 → 64. This demonstrates how numbers below base become smaller.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj--CBgfiHU5jA0vaDfIE1uTUnpH5pITGUH7W6j6IEmvRfoyJRfCOMZkBHk1-1wCDl3NIm4-omLCxIPL_cgLCiXEWiRzJv9iNZhNs0fxJlcppico5HV_c5Ksn0ml0vYzBVK_3PsZWcNg1boBTsupuhiB_KNh_Bxk75i9mFtZ7B5AHh25-HzysF-ckoml0Q/s16000/Slide4.JPG" }, { title: "Example 2", subtitle: "Square of 6", desc: "10-6=4 → 6-4=2, 4²=16 → 2(1)6= 36. Carry-over concept applied.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhy9Sr0dhWQ8mYtzj1ErnZM37xiWCDsmXqKUDSHR_qirUz3RYZCYk4suUE3db2lCCqJY_4jq21Lw5YcpcLUahKHmzmxKys5HYPn_41d38l1hjx25P0XTPfdqMZn4inluYiRgHtIMHfMX1N-MS6lurKYZamGH6auWo484CzSYlSqYioT6SIcOzziSWXOmss/s16000/Slide5.JPG" }, { title: "Base 10 Rule", subtitle: "Near 10", desc: "Step 1: Find deficit/excess. Step 2: Subtract/Add the same from number. Step 3: Square deficit/excess. Step 4: Combine. Quick mental math!", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9hESdE-RBQrRJaWuuSM1HtoN42q6L9kUt-woXkrYWppxTO1O4SPInCrqoa1uhBGw7bXODE_TSx_Rkmebr5elZ1tOlpFN2vMdxbuSF6UVSMDtC1faChFWqLsAu7E1KdyBtwf24iFFRvcTOcLicu6x96UQj5r8DKQy0P9N8xEOexzJT2g675toJW6cBDnU/s16000/Slide6.JPG" }, { title: "96²", subtitle: "Base 100", desc: "Deficit 4 → 96-4=92, 4²=16 → 9216. Perfect for competitive exams where numbers near 100 appear often.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ5IekQBsrU3WhsQ9X0LgCikCPlN2PeRfdccR8FmUV9sfJOiRkV9_ElilXTuUerEnwZVvpLSgXmviiReGvmSlKyrYs9_Utk08T_9eJeZ3CQ_4pNtLHa5ARa541ayJrUraj1bck7v4ZrRS6opr552DYl3QD8gSfrglkuuXbDWq9PRvSzYjd-Otmx-q-7Jc/s16000/Slide7.JPG" }, { title: "103²", subtitle: "Excess 3", desc: "103+3=106, 3²=09 → 10609. For numbers above base, we add the excess.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5RvDBicKrFt_VJE4RAMfpsPaNYV9Hyh2SLzHOybtXh2LbQqt89A0jsMV8nJolumwgtkP_2jCJ_W4LGV7zi3ItzspZBa_ftStmUfw7SYjaqQpevJdG5q--FP0lQSGatI2DHJDpUb5ASpZ6kBmMKsX4vCDdx8j50hjWSgWJ3-mejzCi-qhBsNMTXLYpLH0/s16000/Slide8.JPG" }, { title: "1011²", subtitle: "Base 1000", desc: "1011+11=1022, 11²=121 → 1022121. Multi-digit base extension.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVcR8EoR2p9WU0F_gbIHip5Cq6TAEQ8PanLBCjupMC54KA7t4uPVfpdEz5BIaiTSJACbB__I5KwKJNV4xdQKAkYYAb08buk9uQ_RQRZ4BtntzXUkUAkaA8itK4rgtTN0nFyccDDtcyn1IHzWGSEHgFb_vUYE_hYU7yz0nC6MC0JxhAigKePoGUru3NsiQ/s16000/Slide9.JPG" }, { title: "991²", subtitle: "Deficiency 9", desc: "991-9=982, 9²=81 → 982081. Note: placeholders are important (081).", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuHKUEPUZYIbuYT-VWYgVnvByRq1eF27C_vvQ2fdUjKCeDeWs6_FPccRTkMSi_59StwJ79z9gXK2bhqHWdQiewGWdt74lHHW4njKhEo9l77u37e8hjCHFyFGZHVpFjmCtcAN8FRlrr6g2d847oAywj7crL85WVTVoLDEa9aVW-6zA7uD33DJRQGlSymJY/s16000/Slide10.JPG" }, { title: "93² & 88²", subtitle: "Carry over", desc: "93²=8649 ; 88²=76/144 → 7744 (carry 1 from 144).", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfFJUGlGGPNU0lSYFMB7JXCrklLFfOK7teKuRBqbMWzyIlO2S9ROInADCgAub_c0NDfPV69OBkS-ZOljYs7azS0QQX_AjHbfIlBAVk0C8uvWls4clAgYWbiavnNgWY3KuMLnkFEvJH5eIOt2drGQ8gMR81hMExVpaGQ1WiuGL47RLbCPgy_63HAsG5fDQ/s16000/Slide11.JPG" }, { title: "Ending with 5", subtitle: "Extended", desc: "45² = 2025, 125² = 15625, 995² = 990025. Universal rule: multiply prefix by its successor, suffix 25.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-Fo8AWQauvsY1XEWnHJaDjv6l5EX2LeMkoB69Xw0VFGeSbgYOrdcwh0W4Dm4fFdKEkwuCUl1JLgv3_3WeG1FmlQq2UnqhVjsDVBelGwi3_1-y7lVOV3jma3IZBVtQ0DgnAvs6Iux7s-rcrvtdQnqOGgqN-UeylY38hOPoh5EyQ8KvnqDiWXrM13F5uyI/s16000/Slide12.JPG" }, { title: "Dwanda Deep", subtitle: "Duplex for 3456", desc: "D(3456)=2×3×6+2×4×5=36+40=76. Step towards squaring large numbers.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjg4OUP6aS2nEIH9lk5hWQLxggGAKI2cgHVkXIw4ouK6zRthAUfT-mr4OnN_2Pj_3NQk6X116N07N_jphs0rfltklf6fVk8yQqmBlTBnM3Tz4AH9yf0SIKIK61PbEls6eGmuwZ8rgxF7j2qF8sF6Ux1iAdBleT63BAHE2PkXMBBYzbjxjjK5LAoUYaoJP8/s16000/Slide13.JPG" }, { title: "1221 Square", subtitle: "Dwanda Yoga", desc: "D(1)=1, D(12)=4, D(122)=8, D(1221)=10, D(221)=8, D(21)=4, D(1)=1 → 1490841.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1TJKxWfD-gCSgUF8caLkScmiQHbBY6YPZloGFYbip-gVFWvtXqgQWZtZcODpfZhlbQizR1OKXdRfwPOE1MvOSaBnsLM5noioPBLj8FI__yimB47TzKGNA2hiaS3akefCOGx4BU-5rOcWxA0d1TuKz6-s0fdb_H90nPt19rcMatG1vHsA7kHMoCtEt7nI/s16000/Slide14.JPG" }, { title: "17²", subtitle: "Starting with 1", desc: "1x1 / 2x7 / 7x7 = 1/14/49 → 289. General method for teens.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigM2PFjAOqumOUOO-DLqVJ9ABdM299Adx0Fm_1k8_iZYe1e5yAygeO-H6j6m6k2U6dy0n1-pXZ-oJPkH1NN4gbulUolholvBkinFIeQCbawD6NxaonVWbiy2YkCU9GcMvlimeaWJKSqnbQSUR3JVu05j6Q-mXYLeDqKJrMxAyafbqJF3Mer5Y5KQVq5tI/s16000/Slide15.JPG" }, { title: "18²", subtitle: "Method for 1x", desc: "1/16/64 → 1+2 / 22/4 = 324. Carry-over demonstration.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj91zevcy8rIlohZL7_oxWxeM-vAW0hhw47-8IQ6EGFtoD6Wyt9jSyfNevhDuKnSOcsXRns6vOMjU_WRIoVtm77Dvve5O0YgfZWRv_-MF6P-WmGV4KvSxvheiOUuBjcaCge6cmqlHY9v8zom8EKEZkNH9d7znMwBihRON2R3lzYbA7zdLFsw2RFwDiUGBs/s16000/Slide16.JPG" }, { title: "Yavadunam Recap", subtitle: "Sub-sutra", desc: "Whatever the deficiency subtract that deficit and write alongside square of deficiency. Core of base method.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5njEmvXjlhqavf1XhPCo1idax0u6bYb3DcaKvRC3Mk8NkQJ_VY4Ee5bQvELgRSY6pa20XAyTiv4hA3curu1JO5SDY_lXkOT8NQd4ad7al4uBGqaWen6SUDk0dU5zYjFRB8vgEwqx-0ZOSxOsnujOMuWMGiXQ2ePSy1tW1ohoCCwQOcryo1t-n91QWQgA/s16000/Slide17.JPG" }, { title: "Base 50 Trick", subtitle: "Advanced Yavadunam", desc: "48²: 48-2=46, 2²=4 → 2304. Using 50 as working base.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRkqSEZyQhU-JOpE2NnykJ8wdvsl0CLJJOZWSjDIo7LXnD3xq4hOKPBZ18oYCf04TFtST2dMmh0qvHAE2s_kBgkbIlLdztB6Zuy7vhbC49NBimMjLdsOrWSuOqdwYdvQzuIkmox6X6oYwzvm4fQHvytb8pcURUDUBrhaTasqwRrJFDvE7wlh5W_FMaAcI/s16000/Slide18.JPG" }, { title: "Dwanda 4-digit", subtitle: "Urdhva style", desc: "Duplex method generalizes to any length. Perfect for squares of 4-digit numbers in exams.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjx_VnasYIw6Yq62a8cW8lOKVBMMoYo3BUZDGXWBRm7lSpq_nKetDg47C8VzV7OdneSncyZdwHmd7ZWkv2H88AT-q4ms9SQbFO7PLbL50uk1a2BCcvXfTu4ZnYzFyk_aSaITopDvJWkkk5XAYiYSkTOPJEdZxRMBNr36GgSNWZpIeYj37sy77H5hMRpsME/s16000/Slide19.JPG" }, { title: "125²", subtitle: "Ekadhikena", desc: "12×13=156, append 25 → 15625. Works for any number of digits ending with 5.", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5_1WiO_gDL0nhtDbQi-a0i9pQKaox2GY5HhoDLAIFnn9U0nB39Hd5JDqVsm7fnn9gL2JDfW3i2uW-adl-XUpYdLfnXUUqQbCOJCGY33ommu6bjYOm7MYxq5Ky_CEogluW3-0M_kCA397IkpXTCWRPjfWnCH3I6h8HgULRF0HbKnt2DuhxA1-D2NHXIxM/s16000/Slide20.JPG" }, { title: "Vedic Squaring Summary", subtitle: "All Three Sutras", desc: "✅ Yavadunam (base proximity) ✅ Ekadhikena (ending with 5) ✅ DwandaYoga (general duplex). Practice daily for mental math mastery!", img: "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7VHv62cMmXBL1VkN0rer8qkQzp2sORiIodcBwhBJdtdo6rPKIhujfSRJza8QrHPWRJ6Budm08XDiK0NtGxRGUD5Pk2rLTe_UysrAcozhDGIwJzGzvyyyBqMvYK4N9m67HoUsd5P-aZCep3r9CzkZl3eMOHxJd14Ts6_-vPEGa0lLq6zmNeeJWxzxvkc8/s16000/Slide21.JPG" } ];

 VEDIC MATHEMATICS

MULTIPLICATION just ABOVE THE BASE

BASE 10

Write above the base 10

Put the sign +

Now separate L / R

LEFT part cross addition

Right hand part vertically multiply 

 the two digits and should be only 1 place

MULTIPLICATION just ABOVE THE BASE

BASE 10

EXTRA SUMS

16 x 19 = ____

13 X 14 = ____

15 X 18 = ____

16 X 17 = ____

17 X 19 = ____

BASE 100

Write above the base 100

Put the sign +

Now separate L / R

LEFT part cross addition

Right hand part vertically multiply 

 the two digits and product should write

By 2 places 

So carry over to the next place

BASE 100

EXTRA SUMS

106 x 109 = ____

103 X 104 = ____

105 X 108 = ____

106 X 107 = ____

107 X 109 = ____

BASE 1000

Write above the base 100

Put the sign +

Now separate L / R

LEFT part cross addition

Right hand part vertically multiply 

 the two digits and product should write

By 3 places 

Like the above Examples we can find for bases 10, 100, 1000, 10000, etc..

TWO NUMBERS SHOULD just more than THE BASE

Try Yourself

Do Multiplication within Minute by mind calculation without any paper work, 

     calculator etc.,

Surprise others

WATCH IT ON YOUTUBE : CLICK HERE

Play & Learn with your Friends Kutties! 👍

All the best! 

Thank You🙏🏻

 VEDIC MATHEMATICS

MULTIPLICATION just ABOVE THE BASE

BASE 10

Write above the base 10

Put the sign +

Now separate L / R

LEFT part cross addition

Right hand part vertically multiply 

 the two digits and should be only 1 place

MULTIPLICATION just ABOVE THE BASE

BASE 10

EXTRA SUMS

16 x 19 = ____

13 X 14 = ____

15 X 18 = ____

16 X 17 = ____

17 X 19 = ____

BASE 100

Write above the base 100

Put the sign +

Now separate L / R

LEFT part cross addition

Right hand part vertically multiply 

 the two digits and product should write

By 2 places 

So carry over to the next place

BASE 100

EXTRA SUMS

106 x 109 = ____

103 X 104 = ____

105 X 108 = ____

106 X 107 = ____

107 X 109 = ____

BASE 1000

Write above the base 100

Put the sign +

Now separate L / R

LEFT part cross addition

Right hand part vertically multiply 

 the two digits and product should write

By 3 places 

Like the above Examples we can find for bases 10, 100, 1000, 10000, etc..

TWO NUMBERS SHOULD just more than THE BASE

Try Yourself

Do Multiplication within Minute by mind calculation without any paper work, 

     calculator etc.,

Surprise others

WATCH IT ON YOUTUBE : CLICK HERE

Play & Learn with your Friends Kutties! 👍

All the best! 

Thank You🙏🏻

 VEDIC MATHEMATICS
MULTIPLICATION just less than the base

 

NIKHILAM NAVATASHCARAMAM DASATAH

ALL FROM 9 AND THE LAST FROM 10

BASE 10

Write the complements of base 10

Put the sign –

Now separate L / R

LEFT part cross subtraction

Right hand part vertically multiply 

 the two complement digits and 

should be only 1 place

MULTIPLICATION just less than the base

BASE 10

EXTRA SUMS

6 x 9 = ____

7 X 4 = ____

5 X 8 = ____

6 X 8 = ____

8 X 9 = ____

BASE 100

Write the complements of base 100

Put the sign –

Now separate L / R

LEFT part cross subtraction

Right hand part vertically multiply 

 the two complement digits and 

should be only 2 places

BASE 100

EXTRA SUMS

96 x 99 = ____

93 X 94 = ____

95 X 98 = ____

96 X 98 = ____

97 X 99 = ____

BASE 1000

Write COMPLEMENT of the base 1000

Put the sign -

Now separate L / R

LEFT part cross subtraction

Right hand part vertically multiply 

 the two numbers and product should write

By 3 places 

MULTIPLICATION just less than THE BASE

Like the above Examples we can find for bases 10, 100, 1000, 10000, etc..

TWO NUMBERS SHOULD just less than THE BASE

Try Yourself

Do Multiplication within Minute by mind calculation without any paper work, 

     calculator etc.,

Surprise others

WATCH IT ON YOUTUBE : CLICK HERE

Play & Learn with your Friends Kutties! 👍

All the best! 

Thank You🙏🏻