1.

What must be multiplied to (√a+√b) to get a-b?

Answer»

Answer:

√a - √B.

Step-by-step explanation:

Let the required NUMBER X.

 Here,

    Multiplication of ( √a + √b ) and x is a - b.

⇒ ( √a + √b ) * x = ( a - b )

⇒ x = ( a - b ) / ( √a + √b )

  On RHS: multiply as WELL as divide by √a - √b :

⇒ x = ( a - b )( √a - √b ) / ( √a + √b )( √a - √b )

          We KNOW, ( a + b )( a - b ) = a^2 - b^2.

    Thus, ( √a + √b )( √a - √b )

                     =  ( √a )^2 - ( √b )^2

                     = a - b

   So, ( √a + √b )( √a - √b ) = a - b

Continued  :

⇒ x = ( a - b )( √a - √b ) / ( a - b )

⇒ x = √a - √b

        Hence the required number is √a - √b.


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