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: \(\sqrt{2 \cdot 6.36 \cdot {10}^{6} \cdot 335}\)

MathBot Answer:

\[\sqrt{2 \cdot 6.36 \cdot {10}^{6} \cdot 335} = 200 \sqrt{106530} \approx 65277.86761223132968769337200339974616\]


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