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23x2=4.82\frac{2}{3}x^2=4.8^2

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Full solution

Q. 23x2=4.82\frac{2}{3}x^2=4.8^2
  1. Write Equation: Write down the given equation.\newlineThe given equation is (23)x2=4.82(\frac{2}{3})x^2 = 4.8^2. We need to find the value of xx.
  2. Calculate Square: Calculate the square of 4.84.8. \newline4.82=4.8×4.8=23.044.8^2 = 4.8 \times 4.8 = 23.04.\newlineSo, the equation now is (23)x2=23.04(\frac{2}{3})x^2 = 23.04.
  3. Multiply to Isolate: Multiply both sides of the equation by 32\frac{3}{2} to isolate x2x^2. \newline(32)⋅(23)x2=23.04⋅(32)(\frac{3}{2}) \cdot (\frac{2}{3})x^2 = 23.04 \cdot (\frac{3}{2}).\newlineThis simplifies to x2=23.04⋅(32)x^2 = 23.04 \cdot (\frac{3}{2}).
  4. Calculate Right Side: Calculate the right side of the equation.\newlinex2=23.04×(32)=23.04×1.5=34.56.x^2 = 23.04 \times \left(\frac{3}{2}\right) = 23.04 \times 1.5 = 34.56.\newlineSo, the equation now is x2=34.56.x^2 = 34.56.
  5. Take Square Root: Take the square root of both sides to solve for xx.x2=34.56\sqrt{x^2} = \sqrt{34.56}. This simplifies to x=34.56x = \sqrt{34.56}.
  6. Calculate Final Value: Calculate the square root of 34.5634.56.x=34.56≈5.878x = \sqrt{34.56} \approx 5.878.So, the value of xx is approximately 5.8785.878.

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