Question

If \( n = \sqrt{\frac{16}{81}} \), what is the value of \( \sqrt{n} \)?

• A. \( \frac{1}{9} \)
• B. \( \frac{1}{4} \)
• C. \( \frac{4}{9} \)
• D. \( \frac{2}{3} \)
• E. \( \frac{9}{2} \)

Hint:

When dealing with square roots, simplify fractions first and then take the square root of the numerator and denominator separately.

Answer 1

The Correct Option is C

Step 1: Simplify the given expression for \( n \).
We are given that \( n = \sqrt{\frac{16}{81}} \), so: \[ n = \frac{4}{9} \] Step 2: Find the square root of \( n \).
The square root of \( n \) is: \[ \sqrt{n} = \sqrt{\frac{4}{9}} = \frac{2}{3} \] \[ \boxed{\frac{4}{9}} \]