What is the value of root 7+ root 5 /root 7_ root 5
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7 + √5 / 7 - √5
Rationalizing the denominator ( 7 - √5 ).
=> ( 7+√5 ) / ( 7-√5 ) × ( 7 + √5 ) / ( 7+ √5 )
=> ( 7 + √5 ) ( 7 + √5 ) / ( 7 - √5 ) ( 7 + √5 )
=> ( 7 + √5 )² / ( 7)² - (√5 )²
=> (7)² + (√5 )² + 2 × 7 × √5 / 49 - 5
=> 49 + 5 + 14√5 / 44
=> 54 + 14√5 / 44
=> 2 ( 27 + 7√5 ) / 44
=> 27 + 7√5 / 22.
Rationalizing the denominator ( 7 - √5 ).
=> ( 7+√5 ) / ( 7-√5 ) × ( 7 + √5 ) / ( 7+ √5 )
=> ( 7 + √5 ) ( 7 + √5 ) / ( 7 - √5 ) ( 7 + √5 )
=> ( 7 + √5 )² / ( 7)² - (√5 )²
=> (7)² + (√5 )² + 2 × 7 × √5 / 49 - 5
=> 49 + 5 + 14√5 / 44
=> 54 + 14√5 / 44
=> 2 ( 27 + 7√5 ) / 44
=> 27 + 7√5 / 22.
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