Given:
P √3Q √5 R √15 S = 1 1 √3 √5

To Find:
The value of P

Solution:
To find the value of P, we need to isolate P on one side of the equation. Let's simplify the given expression step by step.

Step 1:
P √3Q √5 R √15 S = 1 1 √3 √5

Step 2:
Since we have a square root (√) term in the expression, we can simplify it by considering the properties of square roots.

√3 * √5 = √(3 * 5) = √15

So, the expression becomes:

P √15Q R √15S = 1 1 √3 √5

Step 3:
Now, let's multiply both sides of the equation by the reciprocal of √15, which is 1/√15.

(1/√15) * (P √15Q R √15S) = (1/√15) * (1 1 √3 √5)

Simplifying this, we get:

(P/√15) (√15Q/√15) (R/√15) (√15S/√15) = (1/√15) (1/√15) (√3/√15) (√5/√15)

Step 4:
Now, let's simplify the expression by removing the square roots from the denominators.

(P/√15) Q (R/√15) S = (1/√15) (1/√15) (√3/√15) (√5/√15)

Simplifying further, we get:

(P/√15) Q (R/√15) S = 1/15 1/15 √3/15 √5/15

Step 5:
Since the left side of the equation is a product of four terms and the right side is a product of four terms, we can equate the corresponding terms.

P/√15 = 1/15

Simplifying this, we get:

P = √15/15

Step 6:
To simplify further, we can rationalize the denominator (√15) by multiplying the numerator and denominator by √15.

P = (√15 * √15) / (15 * √15)

Simplifying this, we get:

P = 15 / 15√15

Step 7:
To simplify the expression further, we can multiply the numerator and denominator by √15.

P = (15 * √15) / (15 * √15 * √15)

Simplifying this, we get:

P = 15√15 / 15 * 15

Step 8: