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Find 4x3\sqrt{4x^{3}} at x=4x=4.

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Full solution

Q. Find 4x3\sqrt{4x^{3}} at x=4x=4.
  1. Identify Expression and Value: Identify the expression to be simplified and the value of xx. We need to find the square root of 4x34x^{3} and we are given that x=4x=4.
  2. Substitute Value: Substitute the value of xx into the expression.4x3\sqrt{4x^{3}} becomes 4×43\sqrt{4\times4^{3}}.
  3. Simplify Inside Square Root: Simplify the expression inside the square root. 434^{3} is 4×4×44\times4\times4, which equals 6464. So, 4×43\sqrt{4\times4^{3}} becomes 4×64\sqrt{4\times64}.
  4. Multiply Inside Square Root: Multiply the numbers inside the square root. \newline4×644\times64 equals 256256.\newlineSo, 4×64\sqrt{4\times64} becomes 256\sqrt{256}.
  5. Find Square Root: Find the square root of 256256. The square root of 256256 is 1616, because 16×1616\times16 equals 256256.

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