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Simplify. \newline925\sqrt{\frac{9}{25}}\newline_____________

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Q. Simplify. \newline925\sqrt{\frac{9}{25}}\newline_____________
  1. Apply Quotient Rule: Apply the quotient rule of radicals to the expression 925\sqrt{\frac{9}{25}}. According to the quotient rule, the square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator. Therefore, 925\sqrt{\frac{9}{25}} can be written as 9/25\sqrt{9} / \sqrt{25}.
  2. Calculate Square Root of Numerator: Calculate the square root of the numerator, which is 9\sqrt{9}. The number 99 is a perfect square because it can be expressed as 33 times 33. Thus, 9\sqrt{9} equals 33.
  3. Calculate Square Root of Denominator: Calculate the square root of the denominator, which is 25\sqrt{25}.\newlineThe number 2525 is a perfect square because it can be expressed as 55 times 55.\newlineThus, 25\sqrt{25} equals 55.
  4. Divide Square Roots: Divide the square root of the numerator by the square root of the denominator.\newlineWe have found that 9\sqrt{9} is 33 and 25\sqrt{25} is 55.\newlineTherefore, 9/25\sqrt{9}/\sqrt{25} equals 35\frac{3}{5}.