Evaluate
\frac{2\sqrt{3}-1}{7}\approx 0.352014516
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\frac{9-2\times 9\sqrt{3}}{9-2^{3}\times 9}
Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.
\frac{9-18\sqrt{3}}{9-2^{3}\times 9}
Multiply -2 and 9 to get -18.
\frac{9-18\sqrt{3}}{9-8\times 9}
Calculate 2 to the power of 3 and get 8.
\frac{9-18\sqrt{3}}{9-72}
Multiply 8 and 9 to get 72.
\frac{9-18\sqrt{3}}{-63}
Subtract 72 from 9 to get -63.
Examples
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y = 3x + 4
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}