Correct Option: D

Let us assume
P = √1 + a + √1 - a
Square on both side,
P ² = ( √1 + a + √1 - a ) ²
Use the formula ( a + b ) ² = a ² + b ² + 2ab
we will get
⇒ P ² = (1 + a) + (1- a) + 2 √1 + a x √1 - a
⇒ P ² = (1 + a) + (1- a) + 2 √(1 + a ) x ( 1 - a )
⇒ P ² = 2 + 2 √1 - a²
⇒ P ² = 2 (1 + √1 - a²)
Now put the value of a which is given in question;
⇒ P ² = 2 (1 + √1 - ( √3/2 )²)
⇒ P ² = 2(1 + √1 - 3/4 )
⇒ P ² = 2(1 + √1/4 )
⇒ P ² = 2(1 + 1/2) = 2 x 3/2 = 3
⇒ P= √3
∴ (√1 + a + √1 - a) = √3