Question

hey! frnds solve this

Answer 1

(1)

$Given : \frac{ \sqrt{7} }{ \sqrt{23} - \sqrt{78} }$

$= \ \textgreater \ \frac{ \sqrt{7} }{ \sqrt{23} - \sqrt{78} } * \frac{ \sqrt{23} + \sqrt{78} }{ \sqrt{23} + \sqrt{78} }$

$= \ \textgreater \ \frac{ \sqrt{7}( \sqrt{23} + \sqrt{78}) }{ \sqrt{23} - \sqrt{78} }$

$= \ \textgreater \ \frac{ \sqrt{7}( \sqrt{23} + \sqrt{78}) }{( \sqrt{23})^2 - ( \sqrt{78})^2 }$

$= \ \textgreater \ \frac{ \sqrt{7}( \sqrt{23} + \sqrt{78}) }{23 - 78}$

$= \ \textgreater \ \frac{ \sqrt{7}( \sqrt{23} + \sqrt{78} ) }{-55}$



(2)

$= \ \textgreater \ \frac{41 + \sqrt{7} }{ \sqrt{9} - 3 }$

$= \ \textgreater \ \frac{41 + \sqrt{7} }{3 - 3}$

$= \ \textgreater \ \frac{41 + \sqrt{7} }{0}$

Undefined.



(3)

$Given : \frac{ \sqrt{6} - \sqrt{25} }{ \sqrt{6} - 2 \sqrt{4} }$

$= \ \textgreater \ \frac{ \sqrt{6} - 5 }{ \sqrt{6} - 4 } * \frac{ \sqrt{6} + 4 }{ \sqrt{6} + 4 }$

$= \ \textgreater \ \frac{( \sqrt{6} - 5)( \sqrt{6} + 4) }{( \sqrt{6} - 4)( \sqrt{6} + 4) }$

$= \ \textgreater \ \frac{-14 - \sqrt{6} }{-10}$

$= \ \textgreater \ \frac{14 + \sqrt{6} }{10}$



Hope this helps!

Answer 2

Hey Mate !

Here is your solution :

1.

= √7 ÷ ( √23 - √78 )

Multiplying in numerator and denominator by ( √23 + √78 ).

= [ √7 ( √23 + √78 ) ] ÷ [ ( √23 - √78 ) ( √23 + √78 ) ]

Using identity :

[ ( a + b ) ( a - b ) = a² - b² ]

= [ √7 ( √23 + √78 ) ] ÷ [ ( √23 )² - ( √78 )² ]

= √7 ( √23 + √78) ÷ ( 23 - 78 )

= √7 ( √23 + √78 ) ÷ ( -55 )

= - √7 ( √23 + √78 ) / 55

2.

= ( 47 + √7 ) ÷ ( √9 - 3 )

= ( 47 + √7 ) ÷ ( ±3 - 3 )

When +3,

= ( 47 + √7 ) ÷ ( 3 - 3 )

= ( 47 + √7 ) ÷ 0

Not defined.

When, -3,

= ( 47 + √7 ) ÷ ( -3 - 3 )

= ( 47 + √7 ) ÷ ( -6 )

= - ( 47 + √7 ) / 6

3.

= ( √6 - √25 ) ÷ ( √6 - 2 √4 )

= ( √6 - 5 ) ÷ ( √6 - 4 )

By multiplying in numerator and denominator by ( √6 + 4 ),

=[ ( √6 - 5 ) ( √6 + 4 ) ] ÷ [ ( √6 - 4 ) ( √6 + 4 ) ]

Using identity :

( a + b ) ( a - b ) = ( a² - b² )

= [ √6 × √6 + 4 √6 - 5 √6 - 20 ] ÷ [ ( √6 )² - ( 4 )² ]

= ( 6 - √6 - 20 ) ÷ ( 6 - 16 )

= ( - √6 - 14 ) ÷ ( - 10 )

= - ( √6 + 14 ) ÷ ( -10 )

= ( √6 + 14 ) / 10

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Hope it helps !! ^_^