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Simplify.\newlineRemove all perfect squares from inside the square roots. Assume \newlinexx and \newlinezz are positive.\newline72x3z3=□\sqrt{72x^{3}z^{3}}=\square

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. Simplify.\newlineRemove all perfect squares from inside the square roots. Assume \newlinexx and \newlinezz are positive.\newline72x3z3=□\sqrt{72x^{3}z^{3}}=\square
  1. Identify and Factorize: Identify and factorize the numbers and variables inside the square root to simplify the expression. 72x3z3=36×2×x2×x×z2×z\sqrt{72x^{3}z^{3}} = \sqrt{36 \times 2 \times x^2 \times x \times z^2 \times z}
  2. Break Down Components: Break down the square root into separate components, extracting the perfect squares.\newline= 36×2×x2×x×z2×z\sqrt{36} \times \sqrt{2} \times \sqrt{x^2} \times \sqrt{x} \times \sqrt{z^2} \times \sqrt{z}\newline= 6×x×z×2xz6 \times x \times z \times \sqrt{2xz}
  3. Combine and Simplify: Combine the terms outside the square root and simplify the expression.\newline=6xz×2xz= 6xz \times \sqrt{2xz}

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