Question

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

Answer 1

Answer:

(√a-√b)

Step-by-step explanation:

(√a+√b) (√a-√b) = ((√a) (√a) -(√b) (√b) ) = a-b

Answer 2

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.