square root of 2 times (6.36 times 10 to the power of 6) times by 335

asked by guest
on Jan 12, 2025 at 6:06 am



You asked:

Evaluate the expression: 2⋅6.36⋅106⋅335\sqrt{2 \cdot 6.36 \cdot {10}^{6} \cdot 335}

MathBot Answer:

2⋅6.36⋅106⋅335=200106530≈65277.86761223132968769337200339974616\sqrt{2 \cdot 6.36 \cdot {10}^{6} \cdot 335} = 200 \sqrt{106530} \approx 65277.86761223132968769337200339974616

2⋅6.36⋅106⋅335=2⋅(6+36100)⋅106⋅335=2⋅(6+925)⋅106⋅335=2⋅15925⋅106⋅335=2⋅15925⋅1000000⋅335=31825⋅1000000⋅335=12720000⋅335=4261200000=200⋅106530\begin{aligned}\sqrt{2 \cdot 6.36 \cdot {10}^{6} \cdot 335}&=\sqrt{2 \cdot \left(6 + \frac{36}{100}\right) \cdot 10^{6} \cdot 335}\\&=\sqrt{2 \cdot \left(6 + \frac{9}{25}\right) \cdot 10^{6} \cdot 335}\\&=\sqrt{2 \cdot \frac{159}{25} \cdot 10^{6} \cdot 335}\\&=\sqrt{2 \cdot \frac{159}{25} \cdot 1000000 \cdot 335}\\&=\sqrt{\frac{318}{25} \cdot 1000000 \cdot 335}\\&=\sqrt{12720000 \cdot 335}\\&=\sqrt{4261200000}\\&=200 \cdot \sqrt{106530}\end{aligned}

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