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