Question2: Rationalize the denominators of the following:
-Shresthi Goyal, Subject Matter Expert at Edumarz
(i) 1/√7
Multiplying numerator and denominator by √7
(1/√7) × (√7/√7)
= (1×√7) / (√7×√7)
= √7/7
(ii) 1/ (√7 – √6)
Multiplying numerator and denominator with (√7 + √6)
[1/(√7 – √6)] × [(√7 + √6) / (√7 + √6)]
[1× (√7 + √6)] / [(√7 – √6)(√7 + √6)]
[Since, (a+b) (a−b) =a²- b²]
[(√7 + √6)] / [(√7)² – (√6)²]
= (√7+√6) / (7-6)
= (√7+√6) / 1
= (√7+√6)
(iii) 1/ (√5 + √2)
Multiplying numerator and denominator by (√5 – √2)
[1/ (√5 + √2)] × [(√5 – √2) / (√5 – √2)]
[Since (a + b)(a−b) = a²-b² ]
[(√5 – √2) / (√5 + √2)(√5 – √2)
= (√5 – √2) / [(√5)² – (√2)²]
= (√5 – √2)/ (5-2)
= (√5 – √2)/ 3
(iv) 1/ (√7-2)
Multiplying numerator and denominator by (√7 + 2)
[1/(√7-2)] × [(√7+2)/ (√7+2)]
[Since, (a + b)(a−b) = a² – b²]
= (√7+2)/ [(√7)² – (2)²]
= (√7+2) / ( 7-4)
= (√7+2)/3