Rationalies the denominator and simplify :
(i) √3 - √2 / √3 + √2
(ii)5 + 2√3 / 7+ 4√3 (iii) 1+√2/ 3-2√2,
(iv)2√6 - √5 / 3√5 - 2√6 (v)4√3 + 5√2 / √48 + √18,
(vi)2√3 - √5 / 2√2 + 3√3
Answers
Step-by-step explanation:
if it helped you yo plz mark it as BRAINLIEST
(i) Given : (i) √3 - √2 / √3 + √2
The Rationalisation factor for √3 + √2 is √3 - √2 . Therefore , multiplying and dividing by √3 - √2 we have :
= (√3 - √2) (√3 - √2) / (√3 + √2)(√3 - √2)
= (√3 - √2)²/√3² - √2²
= [√3² + √2² - 2 × √3 × √ 2] / 3 - 2
[By Using Identity : (a - b)² = a² + b² - 2ab & (a + b)(a – b) = a² - b²]
= [3 + 2 - 2√6]/1
= 5 - 2√6
(ii) Given : 5 + 2√3 / 7+ 4√3
The Rationalisation factor for 7+ 4√3 is 7- 4√3 . Therefore , multiplying and dividing by 7 - 4√3 we have :
= (5 + 2√3) × (7 - 4√3) / (7 + 4√3)(7 - 4√3 )
= [5 × 7 - 5 × 4√3 + 2√3 × 7 - 2√3 × 4√3[/ [(7² - (4√3)²]
= [35 - 20√3 + 14√3 - 8 × 3]/[49 - 16 × 3]
= [35 - 6√3 + 14√3 - 24]/[49 - 48]
= [35 - 24 + 6√3 ]/1
= 11 - 6√3
(iii) Given : 1 + √2/ 3 - 2√2
The Rationalisation factor for 3 - 2√2 is 3 + 2√2 . Therefore , multiplying and dividing by 3 + 2√2 we have :
= [(1 + √2) × (3 + 2√2)] / [(3 - 2√2)(3 + 2√2)]
= [3 + 2√2 + 3 × √2 + √2 × 2√2] / [(3)² - (2√2)²]
= [3 + 2√2 + 3√2 + 2 × 2]/ [9 - 4 × 2]
= [3 + 5√2 + 4]/ [9 - 8]
= [3 + 4 + 5√2 ]/ 1
= 7 + 5√2
(iv) Given : 2√6 - √5 / 3√5 - 2√6
The Rationalisation factor for 3√5 - 2√6 is 3√5 + 2√6 . Therefore , multiplying and dividing by 3√5 + 2√6 we have :
= [(2√6 - √5) × (3√5 + 2√6)] / [(3√5 - 2√6 )(3√5 + 2√6)]
= [2√6 × 3√5 + 2√6 × 2√6 - √5 × 3√5 - √5 × 2√6]/[(3√5)² - (2√6)²]
= [6√30 + 4 × 6 - 3 × 5 - 2√30]/[(9 × 5 - 4 × 6]
= [6√30 + 24 - 15 - 2√30]/[(45 - 24]
= [6√30 - 2√30 + 9]/[(21]
= (4√30 + 9)/21
(v) Given : 4√3 + 5√2 / √48 + √18
On simplying the denominator :
√48 + √18 = √16 × 3 + √9 × 2
√48 + √18 = 4√3 + 3√2
The Rationalisation factor for 4√3 + 3√2 is 4√3 - 3√2 . Therefore , multiplying and dividing by 4√3 - 3√2 we have :
4√3 + 5√2 / 4√3 + 3√2
= (4√3 + 5√2) × (4√3 - 3√2) / (4√3 + 3√2)(4√3 - 3√2)
= [4√3 × 4√3 - 4√3 × 3√2 + 5√2 × 4√3 - 5√2 × 3√2]/[(4√3)² - (3√2)²]
= [16 × 3 - 12√6 + 20√6 - 15 × 2]/ [16 × 3 - 9 × 2]
= [48 + 8√6 - 30]/[48 - 18]
= [48 - 30 + 8√6]/30
= (18 + 8√6)/30
= 2(9 + 4√6)/30
= (9 + 4√6)/15
(vi) Given : 2√3 - √5 / 2√2 + 3√3
The Rationalisation factor for 2√2 + 3√3 is 2√2 - 3√3. Therefore , multiplying and dividing by 2√2 - 3√3 we have :
= (2√3 - √5) × (2√2 - 3√3) / [(2√2 + 3√3) (2√2 - 3√3)]
= [2√3 × 2√2 - 2√3 × 3√3 - √5 × 2√2 + √5 × 3√3]/[(2√2)² - (3√3)²]
= [4√6 - 6 × 3 - 2√10 + 3√15]/ [4 × 2 - 9 × 3]
= [4√6 - 18 - 2√10 + 3√15]/[8 - 27]
= [4√6 - 18 - 2√10 + 3√15]/[- 19]
= (18 - 3√15 + 2√10 - 4√6]/19
HOPE THIS ANSWER WILL HELP YOU…..
Some questions of this chapter :
Express each one of the following with rational denominator:
(i) 1/ 3+√2 (ii)1/√6 - √5 (iii) 16/ √41 - 5
(iv)30/ 5√3 - 3√5 (v) 1/ 2√5 - √3 (vi)√3 + 1 / 2√2 - √3 (vii)6 - 4√2 / 6 + 4√2 (viii) 3√2 + 1 / 2√5 - 3 (ix) b² / √a² + b² + a
https://brainly.in/question/15897352
Rationalise the denominator of each of the following (i-vii) :
(i) 3/√5 (ii)3/2√5 (iii)1/√12 (iv) √2/√5 (v) √3 + 1/√2 (vi) √2 + √5 / √3 (vii) 3√2/√5
https://brainly.in/question/15897353