To solve this problem, we will use the properties of square roots and simplify the given expression step by step.

Given: P √3Q √5 R √15 S = 1 1 √3 √5

Simplifying the expression:
P √3Q √5 R √15 S = 1 1 √3 √5

We can rewrite the square roots using their respective indices:
P Q^(1/2) 5^(1/2) R 15^(1/2) S = 1 1 3^(1/2) 5^(1/2)

Now, let's group the like terms together and simplify further:
P R S Q^(1/2) 5^(1/2) 15^(1/2) = 1 1 3^(1/2) 5^(1/2)

We can combine the coefficients on the right side of the equation:
P R S Q^(1/2) 5^(1/2) 15^(1/2) = 1(1) 1(3^(1/2)) 1(5^(1/2))

Simplifying the right side of the equation:
P R S Q^(1/2) 5^(1/2) 15^(1/2) = 1 3^(1/2) 5^(1/2)

Now, we can equate the corresponding terms on both sides of the equation:
P = 1
R = 1
S = 1
Q^(1/2) = 3^(1/2)
5^(1/2) = 5^(1/2)
15^(1/2) = 5^(1/2)

Since the square root of 15 is equal to the square root of 5, we can simplify further:
P = 1
R = 1
S = 1
Q^(1/2) = 3^(1/2)
5^(1/2) = 5^(1/2)

Now, let's square both sides of the equation Q^(1/2) = 3^(1/2):
(Q^(1/2))^2 = (3^(1/2))^2
Q = 3

Finally, substituting the values of P, Q, R, and S back into the original expression:
P √3Q √5 R √15 S
= 1 √3(3) √5 1 √15(3)
= 1 √9 √5 1 √45
= 1 3 √5 1 √45
= 1 3 √5 1 3 √5
= 1 1

Therefore, the value of P is 1.

The correct answer is not (a) 7/11, but rather (a) 1.