Rajasthan Board RBSE Class 10 Maths Chapter 1 Vedic Mathematics Ex 1.2

**By the method of upsutra yavaduham Tavaduram find the square:**

Question 1.

93

Solution

93^{2} = 9(93 + 3)/(3)^{2}

= 9(96)/9 Base = 10

= 864/9 Sub-base = 10 × 9

8649 deviations = + 3

Question 2.

206

Solution

206^{2} = 2(206 + 06)/(06)^{2}

= 2(212)/36 Base = 100

= 424/36 Sub-base = 100 × 2

= 42436 deviation = +06

Question 3.

211

Solution

211^{2} =2(211 + 11)/(11)^{2}

= 2(222)_{1}21 Base = 100

= 444/_{1}21 Sub-base = 100 x 2

= 44521 deviation = +11

Question 4.

405

Solution

405^{2} = 4(405 + 05)/(05)^{2}

= 4(410) / 25 Base = 100

= 1640 / 25 Sub-base = 100 × 4

= 164025 deviation = +05

Question 5.

16

Solution

Question 6.

31

Solution

Question 7.

24

Solution

Question 8.

56

Solution

**By Sutra Ekadhikena Poorvena find the square of the following:**

Question 9.

45

Solution

45^{2} = 4 × 5 / 5 × 5 = 20 / 25 = 2025

Question 10.

85

Solution

85^{2} = 8 × 9 / 5 × 5 = 72 / 25 = 7225

Question 11.

115

Solution

115^{2} = 11 × 12 / 5 × 5 = 132 / 25 = 13225

Question 12.

125

Solution

125^{2} = 12 × 13 / 5 × 5 = 156 / 25 = 15625

**By Sutra Sankaiana – Viyavkalan find the square of the following:**

Question 13.

23

Solution

23^{2} = (23 + 3)(23 – 3) + 3^{2}

= 26 × 20 + 3^{2}

= 520 + 9

= 529

Question 14.

38

Solution

38^{2} = (38 + 8)(38 – 8) + (8)^{2}

= (46 × 30) + 64

= 1380 + 64

= 1444

Question 15.

69

Solution

69^{2} = (69 + 9)(69 – 9) + 9^{2}

= (78)(60) + 81

= 4680 + 81

= 4761

Question 16.

89

Solution

89^{2} = (89 + 9)(89 – 9) + 9^{2}

= (98)(80) + 81

= 7840 + 81

= 7921

**By Dwandwa Yog find the Square:**

Question 17.

362

Solution

Writting five digit groups of then number 362 – 3, 36, 362, 62 and 2 and the dwandwa yog of these five digit groups

Question 18.

453

Solution

Five digit groups of the no. 453 – 4, 45, 453, 53 and 3 Dwandwa yog of these groups

Question 19.

4312

Solution

Seven digit group of the number 4312 – 4, 43, 431, 4312, 321, 12 and 2 Dwandwa yog of these groups

Question 20.

2456

Solution

Seven digit group of the number 2456 – 2, 24, 2456, 456 and 6 Dwandwa yog of these groups

**Find cube by Sutra Nikhilam**

Question 21.

14

Solution

We know that

Question 22.

97

Solution

We know that

Question 23.

27

Solution

base = 10, sub-base = 10 × 2, sub-base digit = 2, deviation = +7

We know that

Question 24.

395

Solution

Here base = 100, sub-base digit = 4, deviation = – 05,

We know that

**By Upsutra Anurupyena find the cube of the following:**

Question 25.

16^{3}

Solution

Question 26.

33^{3}

Solution

Question 27.

41^{3}

Solution

Question 28.

52^{3}

Solution

**Find cube by sutra Ekadhikene purvena**

**Formula:** Square of ten’s digit × It’s more than one/square of ten’s place digit × deviation/3 × ten’s digit × (unit digit)^{2}/(unit digit)^{3}.

where deviation = unit digit × 3 – 10

Question 29.

45

Solution

Question 30.

73

Solution

Question 31.

24

Solution

Question 32.

106

Solution

Steps: Deviation = 6 × 3 ~ 10 = 8