Name: Aman Chaudhary Class: 8th Section: B Shree Ji Baba Saraswati Vidya Mandir Senior Secondary School Mathura. Name: Aman Chaudhary Class: 8th Section: B

Vedic Ganit:- Introduction: Vedic Ganit is the collection of easy mathematic sutra by which we can solve mathematical question/problems easily. We also find solution orally. It help me in examination time to calculate multiplication, division etc. in less time.

Vedic Ganit help me in my mathematics syllabus in following Topic:- Multiplication Division Square Cube & Cube root

Multiplication:- The Sutra are:- 1. Nikhilam Navatas’caramam Das’atah In multiplication Two Sutra are use. The Sutra are:- 1. Nikhilam Navatas’caramam Das’atah 2. Urdhva-tiryagbhyam Example by Nikhilam Navatas’caramam Das’atah:- 91 multiply by 91. By general method. By Vedic method- Nikhilam Navatas’caramam Das’atah 91*91 91-9 91 91-9 819* 82/81 8281 In this method, Firstly we are count the complement of 91-9;second,add them ; third, subtract the sum from nearest base-100 and multiply the complement . So, answer is 8281. 56 multiply by 98. By general method. By Vedic method-Nikhilam Navatas’caramam Das’atah 56*98 56-44 448 98- 2 504* 54/88 5488 In this method, Firstly, we are count the complement of 56-44 & 98-2;second, add them ; third , subtract the sum from nearest base-100 and multiply the complement. So, answer is 5488.

Example by Urdhva-tiryagbhyam:- 12 multiply by 11. By General method. By Vedic Ganit method- Urdhva-tiryagbhyam. 12*11 12 12 *11 12* 1/1+2/2 132 =132 23 multiply by 21. By General method. By Vedic Ganit method- Urdhva-tiryagbhyam. 23*21 23 23 *21 46* 4/2+6/3 483 =483

Division:- In division, we are use Dhwajanka method. For example :- 98374 divided by 87. By general method. By Vedic Ganit method-Dhwajanka. 87)98374(1130.8 87 9837:4 87 1130:8 113 87 In this method , we are imagine Dhwaj of first digit 267 of divider. After we divide 9 by 8 i.e. 1 and 1 261 reminder. After we subtract 7*1 from 18 and divide 640 answer by 8 i.e. (18-7)/8=1 and 3 reminder. After we subtract 7*1 from 33 and divide answer by 8 i.e. (33-7)/8=3 and 2 reminder. After we subtract 7*3 from 27 and divide answer by 8 i.e. (27- 21)/8=0 and 6 reminder. After we subtract 7*0 from 64 and divide by 8 i.e. (64-0)/8=8. So, answer is 1130.8

Square:- We are use Yavdunam Sutra to calculate square. For Example:- Square of 997. =994/009 =994009 In this method, first, we are subtract number from nearest base-1000 i.e.1000-997=3; second, calculate square of 3 in three digit : we get first part i.e. 009 & to find last part, subtract 3 from number i.e. 997-3=994. So, number =994009.

Square of 113. =126/169 =12769 There number is larger than nearest base. So, first, we are subtract nearest base-100 from number i.e.113-100=13; second, calculate square of 13 in two number : we get first part i.e. 69 and 1 carry & to find another part, add 13 to number i.e. 13+113=126 and add carry. So, number =12769.

Cube:- For Example:- We are use Yavdunam Sutra to calculate cube. Cube of 104. =112/48/64 =1124864 In this method, first, we find nearest base-100, there number is larger than nearest base. So, second, subtract nearest base from number i.e. 104-100=4 & we find mass. To find first part, we write cube of mass i.e. 43=64; to find next part, we multiply mass*mass*3 i.e. 4*4*3=48 & to find last part, add number to 2*mass i.e. 104+2*4=112. So, number is 1124864.

Cube of 996. = 988/048/064 =988047936 In this method, first, we find nearest base-1000, there number is smaller than nearest base. So, second, subtract number from nearest base i.e. 1000-996=4 & we find mass. To find first part, we write cube of mass i.e. 43=064; to find next part, we multiply mass*mass*3 i.e. 4*4*3=048 & to find last part, subtract 2*mass from number i.e. 996-2*4=998. There number is smaller than nearest base. So, we subtract first part from nearest base i.e. 1000-064=936 & subtract 1from second part i.e. 048-1=047. Note: This type question we subtract carry of first part from second part.

Cube root:- For example:- Cube root of 32768. Step 1 From groups of three starting from the rightmost digit of 32768.32 768.In this case one group i.e., 768 has three digits whereas 32 has only two digits. Step 2 Take 768. One’s place of cube of 8 is 2. So, we take the one’s place of the required cube root as 2. Step 3 Take the other group, i.e., 32. Cube of 3 is 27 and cube of 4 is 64. 32 lies between 27 and 64. The smaller number among 3 and 4 is 3. Take 3 as ten’s place of the cube root of 32768. Thus, cube root of 32768 is 32.