Question

If \(n = \frac{16}{81}\), what is the value of \(\sqrt{n}\)?
*(Note: The OCR included a typo, which has been corrected to the most logical question based on the options.)*

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

Hint:

Memorizing perfect squares (like \(4^2=16\), \(9^2=81\), etc.) is essential for saving time on arithmetic and algebra problems on standardized tests.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The problem asks to find the square root of a given fraction. The square root of a fraction is the square root of the numerator divided by the square root of the denominator.
Step 2: Key Formula or Approach:
The property of square roots we use is: \[ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \] Step 3: Detailed Explanation:
We are given \(n = \frac{16}{81}\) and we need to find \(\sqrt{n}\).
Substitute the value of n: \[ \sqrt{n} = \sqrt{\frac{16}{81}} \] Apply the square root property: \[ \sqrt{\frac{16}{81}} = \frac{\sqrt{16}}{\sqrt{81}} \] Calculate the square roots of the numerator and the denominator: \[ \sqrt{16} = 4 \] \[ \sqrt{81} = 9 \] Combine the results: \[ \sqrt{n} = \frac{4}{9} \] Step 4: Final Answer:
The value of \(\sqrt{n}\) is \(\frac{4}{9}\).