class ch. 01

Q. Convert the given rational numbers in decimal form:

Q. Find four rational numbers between 7 and 9.

Q. Find three rational numbers between 3/4 and  4/3.

Q. convert the given rational numbers in decimal form:

Q. Expression of Decimal numbers in the form of p/q:

(i) Expression of Decimal numbers 2.45 in the form of p/q

(ii) Expression of Decimal numbers 3.333... in the form of p/q.

Q. Add 2√3 + 4√5 and 3√3 - 7√5

Sol. (2√3 + 4√5) + (3√3 - 7√5) 

= (2√3 +3√3) + (-7√5 + 4√5)

= 5√3 - 3√5

Q. Multiply 2√3 by 3√5

Sol. 2√3 × 3√5 

= 2 × 3 × √3 ×√5

= 6√15

Q. Divide 8√20 by 2√5

Sol. 8√20 ÷ 2√5 

= 8√20 / 2√5

= 4 × √4 

= 8

Q. Simplify the following expressions:

(√2 + √3) (√5 - √7) 

= √2 (√5 - √7) + √3) (√5 - √7) 

= √2 √5 - √2 √7 + √3 √5 - √3 √7

= √10 - √14 + √15 - √21

Task 31: Check your understanding:

Q.1 Add (3√5 + √3) , (-3√5 + 5√3)

Q.2 Subtract (√5 + 7√3) from ( 2√5 - √3)

Q.3 Multiply 3√5 and 5√3

Q.4 Divide 6√10 and 3√2

Q.5 Simplify the following expressions:

(i) (3√5 + √3) (3√5 - √3) 

(ii) (3√5 + √2) (√5 - 2√3)

(iii) ( √7 - √3)²

(iv) (√11 + √2) (√11 - 2√2)

(v) ( √2 + 3) ( √2 - 3)

Rationalize

(i) 1/√2

(ii) 1/√5

(iii) ( 1/√3

(iv) (2√11

(v) 3√2/√2

(vi) 2√2/√5

(vii) 6/√3

(viii) 12√2/3√3

Rationalize

(i) (3+√2)/√2

(ii) (3+√2)/(√2+3)

(iii) ( 1/√3

(iv) (2√11

(v) 3√2/√2

(vi) 2√2/√5

(vii) 6/√3

(viii) 12√2/3√3

(3, 4, 5) (5, 12, 13) (6, 8, 10) (7, 24, 25) (8, 15, 17) (9, 40, 41) (11, 60, 61)  (12, 35, 37) (13, 84, 85) (15, 112, 113) (16, 63, 65) (17, 144, 145) (20, 21, 29)   (28, 45, 53)  (33, 56, 65) (48, 55, 73) (36, 77, 85) (39, 80, 89) (65, 72, 97)

पांच सबसे आम पायथागॉरियन त्रिक कौन से हैं

(3,4,5)

(5,12,13)
​​(7,24,25)
(9,40,41)

(11,60,61)

पाइथागोरस त्रिक कभी भी सभी विषम संख्याओं या दो सम संख्याओं और एक विषम संख्याओं से नहीं बना होता है

पायथागॉरियन त्रिगुण	x 2 (समय 2)	x 3 (समय 3)	x 4 (समय 4)
3-4-5	6-8-10	9-12-15	12-16-20
5-12-13	10-24-26	15-36-39	20-48-52
7-24-25	14-48-50	21-72-75	28-96-100
9-40-41	18-80-82	27-120-123	36-160-164
11-60-61	22-120-122	33-180-183	44-240-244

पायथागॉरिय