If p and q are perfect squares, then \(\sqrt{\frac{p}{q}} \) is always a rational number. Is the statement true ?

Given:

If p and q are perfect squares, then √(p/q) is always a rational number.

Formula used:

If p = a² and q = b², where a and b are integers, then:

√(p/q) = √(a²/b²) = a/b

Calculation:

Let p = 16 (4²) and q = 9 (3²):

√(p/q) = √(16/9)

⇒ √(16/9) = √(4²/3²)

⇒ √(4²/3²) = 4/3

Since 4/3 is rational, the statement holds true.

∴ The correct answer is option 3).