Chapter 1 Vedic Mathematics Ex 1.3

RBSE Solutions for Class 9 Maths Chapter 1 Vedic Mathematics Ex 1.3

Find a product by using Sutra Ordhva- tiryagbhyam or by Sutra vertically and crosswise.

Question 1.
486 x 26
Solution:

Question 2.
403 x 218
Solution:

Question 3.
906 x 246
Solution:

Question 4.
744 x 314
Solution:

Find the square of the following numbers by Dvanda yoga method or Duplex process.

Question 5.
44
Solution:
(44)2 = (4)2 / 2 x 4 x 4 / (4)2
= 16/32/16
= 16 /3 2 /1 6
= 16 /3 3 / 6
= 1936

Question 6.
368
Solution:
(368)2
= (3)2 / 2 x 3 x 6/ 2 x 3 x 8 + 62/2 x 6 x 8 / (8)2
= 9 / 36 / 84 / 96 / 64
= 9 / 36 / 84 / 96 /6 4
= 9 / 36 / 84 /10 2 / 4
= 9 / 36 /9 4 / 2 / 4
= 9 /4 5 / 4 / 2 / 4
= 135424

Question 7.
1234
Solution:
(1234)2
= (1)2 / 2 x (1 x 2) / 2 x (1 x 3) + 22 / 2 x (1 x 4) + 2 x (2 x 3) / 2 x (2 x 4) + 32 / 2 x (3 x 4) / (4) 2
= 1 / 4 / 6 + 4 / 8 + 12 / 16 + 9 / 24 / 16
= 1 / 4 / 10 / 20 / 25 / 24/ 16
= 1 / 4 /1 0 /2 0 /2 5 /2 4 /1 6
= 1 / 4 /1 0 /2 0 /2 5 /2 5 / 6
= 1 / 4 /1 0 /2 0 /2 7 / 5 / 6
= 1 / 4 /1 0 /2 2 / 7 / 5 / 6
= 1 / 5 / 2 / 2 /  7 / 5 / 6
= 1522756

Question 8
2781
Solution:
(2781)2
= (2)2 / 2 x (2 x 7) / 2 x (2 x 8) + 72 / 2 x (2 x 1) + 2 x (7 x 8) / 2 x (7 x 1) + 82 / 2 x (8 x 1) / (1)2 = 4 / 28 / 32 + 49 / 4 + 112 / 14 + 64 / 16 / 1
= 4 / 28 / 81 / 116 / 78 / 16 / 1 = 4 /2 8 /8 1 / 11 6 /7 8 /1 6 / 1
= 4 /2 8 /8 1 /11 6 /7 9 / 6 / 1
= 4 /2 8 /8 1 /12 3 / 9 / 6 / 1
= 4 /2 8 /9 3 / 3 / 9 / 6 / 1
= 4 /37/3/3/9/6/1 =7/7/3/3/9/6/1 = 7733961

Calculate square root of the following numbers by Dvanda yoga method or Duplex process

Question 9.
23409
Solution:

Therefore square root of 23409 = 153
Steps:
(i) 2 – (1)2  = 1, New dividend = 13
Divisor =1 x 2 = 2
(ii) New dividend =13
Adjusted dividend =13 – 1 x 2 = 11
(iii) 11÷2, Quotient digit = 5, Remainder = 1
(iv) New dividend = 14
Adjusted dividend = 14 – 2 x 2 x 2 = 14 – 8 = 6
(v) 6 ÷ 2 = 3, Remainder = 0
(vi) Final remainder = 9 – 3² = 0

Question 10.
189225
Solution:

Therefore square root of 189225 = 435
Steps:
(i) 18 – (4)² =, 2 New dividend = 29
Divisor = 4 x 2 = 8
(ii) 29 ÷ 8, Quotient digit = 3
Remainder = 5
(iii) New dividend = 52
Adjusted dividend = 52 – (3)²
= 52 – 9 = 43
(iv) 43 ÷ 8, Quotient digit = 5,
Remainder = 3
(v) New dividend = 32, Adjusted dividend
= 32 – Dvanda yoga of 35
= 32 – 3 x 5 x 2 = 2
(vi) Final remainder
= 25 – (Dvanda yoga of 350)
= 25 – (5)² = 0

Question 11.
389376
Solution:

Therefore square root of 389376 = 624
Steps:
(i) 38 – (6)² = 2, New dividend = 29
Divisor = 6 x 2 = 12
(ii) 29 ÷ 12, Quotient digit = 2,
Remainder = 5
(iii) New dividend = 53
Adjusted dividend = 53 – 2² = 49
(iv) 49 ÷ 12, Quotient digit = 4,
Remainder = 1
New dividend = 17 and remainder
= 17 – 2 x 4 x 2 = 1
New dividend =16 and final remainder
= 16 – 4² = 0

Question 12.
1156
Solution:

Therefore square root of 1156 = 34
Steps:
(i) 11 – (3)² = 11 – 9 = 2
New dividend = 25
Divisor 3 x 2 = 6
(ii) 25 ÷ 6, Quotient digit = 4,
Remainder = 1
(iii) Final remainder = 16 – (4)²
= 16 – 16 = 0

Divide the following by Dhwajanka method

Question 13.
4532 ÷ 112
Solution:

Therefore quotient = 40
Remainder = 52 Steps:
(i) 4 ÷ 1, Quotient digit = 4,
Remainder digit = 0
(ii) New Dividend = 05
Dividend adjusted = 5 – 4 x 1 = 1
(iii) 1 ÷ 1, Quotient digit = 1,
Remainder = 0
(iv) New dividend = 13
Dividend adjusted
= 13 – (2 x 4 + 1 x 0)
= 13 – 8 = 5
(v) 5 ÷ 1, Quotient digit = 5,
Remainder = 0
(vi) Last remainder = 2

Question 14.
1234 ÷ 42
Solution:

Therefore quotient = 29 and remainder = 16

Question 15.
98765 ÷ 87
Solution:

Therefore quotient = 1135 and remainder = 20
Steps:
(i) 9 ÷ 8, Quotient digit = 1,
Remainder digit = 1
(ii) New dividend = 18
Adjusted dividend
= New dividend – quotient digit x Dhwajank
= 18 – 1 x 7
(iii) 11 ÷ 8, Quotient digit = 1
Remainder = 3
(iv) New quotient = 37
Adjusted quotient = 37 – 1 x 7 = 30
(v) 30 ÷ 8, Quotient digit = 3,
Remainder = 6
(vi) New quotient = 66
Adjusted quotient = 66 – 7 x 3
= 66 – 21 = 45
(vii) 45 ÷ 8, Quotient digit = 5,
Remainder = 5
(viii) New quotient = 55,
Remainder = 55 – 7 x 5 = 20

Question 16.
2101532 ÷ 879
Solution:

Quotient =  = 2390
Remainder = 832 – 81 – 29 = 722

Divide the following by Paravartya yojayet method:

Question 17.
1154 ÷ 103
Solution:

Quotient = 11, remainder = 21

Question 18.
1358 ÷ 113
Solution:

Quotient =12, remainder = 2

Question 19.
1432 ÷ 88
Solution:

Quotient =16, remainder = 24

Question 20.
14885 ÷ 123
Solution:

Quotient = 121, remainder = 02