September 28, 2024 Frantz

Simplifying Radical Expressions – Square Roots Properties


Simplify the following expression:
\[
\sqrt{\frac{9x^2}{y^3}}
\]

Solution
Step-by-Step Simplification:

  • Separate the square root of a fraction: The square root of a fraction can be written as the square root of the numerator divided by the square root of the denominator:
    \[
    \sqrt{\frac{9x^2}{y^3}} = \frac{\sqrt{9x^2}}{\sqrt{y^3}}
    \]
  • Simplify the numerator: The square root of \(9x^2\) can be simplified:
    \[
    \sqrt{9x^2} = \sqrt{9} \cdot \sqrt{x^2} = 3x
    \]
  • Simplify the denominator: To simplify \(\sqrt{y^3}\), we can break it down:
    \[
    \sqrt{y^3} = \sqrt{y^2 \cdot y} = \sqrt{y^2} \cdot \sqrt{y} = y\sqrt{y}
    \]
  • Put everything together: Now, we can rewrite the simplified expression as:

    \[
    \frac{3x}{y\sqrt{y}}
    \]

    • Final Simplified Expression:
    \(\frac{3x}{y\sqrt{y}}\) is the simplified form of \(\sqrt{\frac{9x^2}{y^3}}\)

    One comment

    Reginald Dieujuste
    October 4, 2024 at 6:31 am

    Good job bro

    Reply

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