Question

Rationalize the following

Answer 1

Hi !

(a) 1/√5 - √4

=> 1/ √5 - √4 × √5 + √4 / √5 + √4

=> ( √5 + √4 ) / ( √5 - √4 ) × ( √5 + √4 )

=> ( √5 + √4 ) / (√5)² - (√4)² [(a+b)*(a-b)²=a²-b²]

=> √5 + √4 / 5 - 4

=> √5 + √4 [ Answer ]

(b) 2/ √11 - √9

Rationalise the denominator √11 - √9 .

=> 2/√11-√9 × √11 + √9 / √11 + √9

=> 2 ( √11 + √9 ) / (√11 - √9 ) × ( √11 + √9 )

=> 2√11 + 2√9 / (√11)² - (√9)²

=> 2√11 + 2√9 / 11 - 9

=> 2√11 + 2√9 / 2

=> Taking 2 as common.

=> 2 ( √11 + √9 ) / 2

=> ( √11 + √9 ) [ Answer ]

(c ) 6 / √21 - √19 [ Solve this one by yourself ]

Answer 2

Answer:

$\boxed{1.) \sqrt{5} + \sqrt{4}}$

$\boxed{2.) \sqrt{11} + \sqrt{9}}$

$\boxed{3.) 3(\sqrt{21} + \sqrt{19})}$

Step-by-step explanation:

Check attachments for more information.

Identities used :

• Only one identity is used in these sums.
• a² - b² = (a+b) (a-b)

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