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}}

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