Question

Rationalize the denominator :
(a)1/7+3√2
(b)7+3√5/7-3√5

Answer 1

Question:-

Rationalize the denominator :

(a)1/7+3√2

(b)7+3√5/7-3√5

Answer :-

1st :- 7-3√2/49-(9×2)

2nd :-

( 7 - 3✓5 ) / ( 7 + 3✓5 )

=> ( 7 - 3✓5 ) / ( 7 + 3✓5 ) × ( 7 - 3✓5 ) / ( 7-3✓5 )

= > ( 7 - 3✓5 ) ( 7 - 3✓5 ) / ( 7 + 3✓5 ) ( 7 - 3✓5)

=> (7-3✓5)² / ( 7)² - (3✓5 )²

We know that,

( A - B)² = (A)² + (B)² - 2AB

And,

( A + B ) ( A - B ) = A² - B².

=> (7)² + (3✓5)² - 2 × 7 × 3✓5 / 49 - 45

=> 49 + 45 - 42✓5 / 4

=> 94 - 42✓5 / 4

=> 2 ( 47 - 21✓5 ) / 4

=> ( 47 - 21✓5 ) /2 [ Answer ]

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