sqrt(((0.0152-0.1352)^2+(0.3754-0.1352)^2+(0.0151-0.1352)^2)/2)

asked by guest
on Apr 25, 2024 at 12:55 pm

You asked:

Evaluate the expression: \(\sqrt{\frac{{\left( 0.0152 - 0.1352 \right)}^{2} + {\left( 0.3754 - 0.1352 \right)}^{2} + {\left( 0.0151 - 0.1352 \right)}^{2}}{2}}\)

MathBot Answer:

\[\sqrt{\frac{{\left( 0.0152 - 0.1352 \right)}^{2} + {\left( 0.3754 - 0.1352 \right)}^{2} + {\left( 0.0151 - 0.1352 \right)}^{2}}{2}} = \frac{\sqrt{17304010}}{20000} \approx 0.20799044449204872065633952033984\]

\[\begin{aligned}\sqrt{\frac{{\left( 0.0152 - 0.1352 \right)}^{2} + {\left( 0.3754 - 0.1352 \right)}^{2} + {\left( 0.0151 - 0.1352 \right)}^{2}}{2}}& = \sqrt{\left(\left(\frac{152}{10000} - \frac{1352}{10000}\right)^{2} + \left(\frac{3754}{10000} - \frac{1352}{10000}\right)^{2} + \left(\frac{151}{10000} - \frac{1352}{10000}\right)^{2}\right) \cdot \frac{1}{2}}\\& = \sqrt{\left(\left(\frac{19}{1250} - \frac{1352}{10000}\right)^{2} + \left(\frac{3754}{10000} - \frac{1352}{10000}\right)^{2} + \left(\frac{151}{10000} - \frac{1352}{10000}\right)^{2}\right) \cdot \frac{1}{2}}\\& = \sqrt{\left(\left(\frac{19}{1250} - \frac{169}{1250}\right)^{2} + \left(\frac{3754}{10000} - \frac{1352}{10000}\right)^{2} + \left(\frac{151}{10000} - \frac{1352}{10000}\right)^{2}\right) \cdot \frac{1}{2}}\\& = \sqrt{\left(\left(- \frac{3}{25}\right)^{2} + \left(\frac{3754}{10000} - \frac{1352}{10000}\right)^{2} + \left(\frac{151}{10000} - \frac{1352}{10000}\right)^{2}\right) \cdot \frac{1}{2}}\\& = \sqrt{\left(\frac{9}{625} + \left(\frac{3754}{10000} - \frac{1352}{10000}\right)^{2} + \left(\frac{151}{10000} - \frac{1352}{10000}\right)^{2}\right) \cdot \frac{1}{2}}\\& = \sqrt{\left(\frac{9}{625} + \left(\frac{1877}{5000} - \frac{1352}{10000}\right)^{2} + \left(\frac{151}{10000} - \frac{1352}{10000}\right)^{2}\right) \cdot \frac{1}{2}}\\& = \sqrt{\left(\frac{9}{625} + \left(\frac{1877}{5000} - \frac{169}{1250}\right)^{2} + \left(\frac{151}{10000} - \frac{1352}{10000}\right)^{2}\right) \cdot \frac{1}{2}}\\& = \sqrt{\left(\frac{9}{625} + \left(\frac{1201}{5000}\right)^{2} + \left(\frac{151}{10000} - \frac{1352}{10000}\right)^{2}\right) \cdot \frac{1}{2}}\\& = \sqrt{\left(\frac{9}{625} + \frac{1442401}{25000000} + \left(\frac{151}{10000} - \frac{1352}{10000}\right)^{2}\right) \cdot \frac{1}{2}}\\& = \sqrt{\left(\frac{9}{625} + \frac{1442401}{25000000} + \left(\frac{151}{10000} - \frac{169}{1250}\right)^{2}\right) \cdot \frac{1}{2}}\\& = \sqrt{\left(\frac{9}{625} + \frac{1442401}{25000000} + \left(- \frac{1201}{10000}\right)^{2}\right) \cdot \frac{1}{2}}\\& = \sqrt{\left(\frac{9}{625} + \frac{1442401}{25000000} + \frac{1442401}{100000000}\right) \cdot \frac{1}{2}}\\& = \sqrt{\left(\frac{1802401}{25000000} + \frac{1442401}{100000000}\right) \cdot \frac{1}{2}}\\& = \sqrt{\frac{1730401}{20000000} \cdot \frac{1}{2}}\\& = \sqrt{\frac{1730401}{40000000}}\\& = \frac{1}{20000} \cdot \sqrt{17304010}\end{aligned}\]

asked 9 days ago

active 9 days ago