Evaluate
-2\sqrt{3}-8\approx -11.464101615
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-2\sqrt{3}-8
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\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1-\left(2\sqrt{3}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{3}-1\right)^{2}.
3-2\sqrt{3}+1-\left(2\sqrt{3}\right)^{2}
The square of \sqrt{3} is 3.
4-2\sqrt{3}-\left(2\sqrt{3}\right)^{2}
Add 3 and 1 to get 4.
4-2\sqrt{3}-2^{2}\left(\sqrt{3}\right)^{2}
Expand \left(2\sqrt{3}\right)^{2}.
4-2\sqrt{3}-4\left(\sqrt{3}\right)^{2}
Calculate 2 to the power of 2 and get 4.
4-2\sqrt{3}-4\times 3
The square of \sqrt{3} is 3.
4-2\sqrt{3}-12
Multiply 4 and 3 to get 12.
-8-2\sqrt{3}
Subtract 12 from 4 to get -8.
\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1-\left(2\sqrt{3}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{3}-1\right)^{2}.
3-2\sqrt{3}+1-\left(2\sqrt{3}\right)^{2}
The square of \sqrt{3} is 3.
4-2\sqrt{3}-\left(2\sqrt{3}\right)^{2}
Add 3 and 1 to get 4.
4-2\sqrt{3}-2^{2}\left(\sqrt{3}\right)^{2}
Expand \left(2\sqrt{3}\right)^{2}.
4-2\sqrt{3}-4\left(\sqrt{3}\right)^{2}
Calculate 2 to the power of 2 and get 4.
4-2\sqrt{3}-4\times 3
The square of \sqrt{3} is 3.
4-2\sqrt{3}-12
Multiply 4 and 3 to get 12.
-8-2\sqrt{3}
Subtract 12 from 4 to get -8.
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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}