सही विकल्प: A

1/√( 11 - 2√30 ) - 3/√( 7 - 2√10 ) - 4/√( 8 + 4√3 ) = 1/√{ ( √6 )² + ( √5 )² - 2 × √6 × √5) } - 3/√{ ( √5 )² + ( √2 )² - 2 × √5 × √2 ) - 4/√{ ( √6 )² + ( √2 )² + 2 × √2 × √6 )
= 1/√( √6 - √5 )² - 3/√( √5 - √2 )² - 4/√( √6 + √2 )²
= 1/( √6 - √5 ) - 3/( √5 - √2 ) - 4/(√6 + √2 )
= ( √6 + √5 )/( √6 - √5 )( √6 + √5 ) - 3( √5 + √2 )/( √5 - √2 )( √5 + √2 ) - 4(√6 - √2 )/(√6 + √2 )(√6 - √2 ) [ हर का परिमेयीकरण करने पर ]
= ( √6 + √5 )/( 6 - 5 ) - 3( √5 + √2 )/( 5 - 2 ) - 4(√6 - √2 )/( 6 - 2 )
= √6 + √5 - √5 - √2 - √6 + √2 = 0
∴ 1/√( 11 - 2√30 ) - 3/√( 7 - 2√10 ) - 4/√( 8 + 4√3 ) = 0
अतः इसका मान 0 होगा ।