9.1 Rationalise the denominator of the following: 3 1 √5 (C) 2√5 7 + 2√6 √3+ √2 (a) (b) (a) 9.2 Find the value of the variables in each of the following: 7 + 3√5 (b) √11+√3 3 3√11 +5√3 4 =- 5+2√5 = (d) 1 + a√5 √7 +√3 √7-√3 b√33 (e) (c) 6√5 +4√7 √45 -√28 6 + √2 6-√2 (f) 6-√2 6+ √2 √6 + √2 √6-√2 = a - b√2

Answers 1

Answer:

i) 1/√7

Dividing and multiplying by √7, we get

1/√7 = (1/√7) × (√7/√7)

= √7/7

ii) 1/ (√7 - √6)

Dividing and multiplying by √7 + √6, we get

1/(√7 - √6) = [1/(√7 - √6)] × (√7 + √6) / (√7 + √6)

Using identity (a + b)(a - b) = (a² - b²)

= (√7 + √6) / (√7)² - (√6)²

= (√7 + √6) / (7 - 6)

= √7 + √6

iii) 1/(√5 + √2)

Dividing and multiplying by √5 - √2, we get

= [1/(√5 + √2)] × (√5 - √2)/(√5 - √2)

Using identity (a + b)(a - b) = (a² - b²)

= (√5 - √2) / (√5)² - (√2)²

= (√5 - √2) / (5 - 2)

= (√5 - √2) / 3

iv) 1/(√7 - 2)

Dividing and multiplying by √7 + 2, we get

1/(√7 - 2) = [1/(√7 - 2)] × (√7 + 2)/(√7 + 2)

Using identity (a + b)(a - b) = (a² - b²)

= (√7 + 2) / (√7)² - (2)²

= (√7 + 2) / (7 - 4)

= (√7 + 2) / 3