Correct Answer - Option 3 : (√a)

^{3} : (√b)

^{3}
**Given:**

The ratio of P and Q is the duplicate ratio of a : b.

**Concept used:**

The duplicate ratio of a : b is a^{2} : b^{2}.

The sub-duplicate ratio of a : b is √a : √b.

**Calculation:**

The given ratio is a: b.

P : Q = a^{2} : b^{2}

Q : R = √(a)2 : √(b^{2})

⇒ a : b

**Step 1:**

**Step 2:**

P : Q : R = a^{3} : ab^{2} : b^{3}

Now P : R = a^{3} : b^{3}

⇒ (a3/2)^{2} : (b^{3/2})^{2}

⇒ ((√a)3)^{2} : ((√b)^{3})^{2}

**∴ The ratio of P : R is the duplicate ratio of (√a)3 : (√b)3.**