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Simplify. Assume xx is greater than or equal to zero.\newline20x3\sqrt{20x^3}

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Full solution

Q. Simplify. Assume xx is greater than or equal to zero.\newline20x3\sqrt{20x^3}
  1. Group Factors: Now, we can group the factors into perfect squares and separate them from those that are not perfect squares. 20x3=22×x2×5×x\sqrt{20x^3} = \sqrt{2^2 \times x^2 \times 5 \times x}
  2. Take Square Root: We can take the square root of the perfect squares, which are 222^2 and x2x^2, and place them outside the square root symbol.\newline22×x2×5×x=2×x×5×x\sqrt{2^2 \times x^2 \times 5 \times x} = 2 \times x \times \sqrt{5 \times x}
  3. Final Simplified Form: The expression is now simplified, and since xx is greater than or equal to zero, we do not need to consider absolute values for xx. The final simplified form is 2x⋅5x2x \cdot \sqrt{5x}.

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