((6)(310)-(36)(64))/( √([(6)266-1296][(6)808-4096] ))

asked by guest
on Nov 22, 2024 at 9:47 am



You asked:

Evaluate the expression: \(\frac{6 \cdot 310 - 36 \cdot 64}{\sqrt{\left(6 \cdot 266 - 1296\right) \cdot \left(6 \cdot 808 - 4096\right)}}\)

MathBot Answer:

\[\frac{6 \cdot 310 - 36 \cdot 64}{\sqrt{\left(6 \cdot 266 - 1296\right) \cdot \left(6 \cdot 808 - 4096\right)}} = - \frac{37 \sqrt{141}}{470} \approx -0.93478863238383603762318713024521\]

\[\begin{aligned}\frac{6 \cdot 310 - 36 \cdot 64}{\sqrt{\left(6 \cdot 266 - 1296\right) \cdot \left(6 \cdot 808 - 4096\right)}}& = \left(6 \cdot 310 - 36 \cdot 64\right) \cdot \frac{1}{\sqrt{\left(6 \cdot 266 - 1296\right) \cdot \left(6 \cdot 808 - 4096\right)}}\\& = \left(1860 - 36 \cdot 64\right) \cdot \frac{1}{\sqrt{\left(6 \cdot 266 - 1296\right) \cdot \left(6 \cdot 808 - 4096\right)}}\\& = \left(1860 - 2304\right) \cdot \frac{1}{\sqrt{\left(6 \cdot 266 - 1296\right) \cdot \left(6 \cdot 808 - 4096\right)}}\\& = -444 \cdot \frac{1}{\sqrt{\left(6 \cdot 266 - 1296\right) \cdot \left(6 \cdot 808 - 4096\right)}}\\& = -444 \cdot \frac{1}{\sqrt{\left(1596 - 1296\right) \cdot \left(6 \cdot 808 - 4096\right)}}\\& = -444 \cdot \frac{1}{\sqrt{300 \cdot \left(6 \cdot 808 - 4096\right)}}\\& = -444 \cdot \frac{1}{\sqrt{300 \cdot \left(4848 - 4096\right)}}\\& = -444 \cdot \frac{1}{\sqrt{300 \cdot 752}}\\& = -444 \cdot \frac{1}{\sqrt{225600}}\\& = -444 \cdot \frac{1}{40 \cdot \sqrt{141}}\\& = - \frac{37}{470} \cdot \sqrt{141}\end{aligned}\]

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