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If a = √3/2, then √1 + a + √1 - a =?

Correct Answer: √3

Explanation:

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


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