Evaluate
2\left(\sqrt{2}+\sqrt{5}+\sqrt{10}+4\right)\approx 21.6251184
Expand
2 \sqrt{2} + 2 \sqrt{5} + 2 \sqrt{10} + 8 = 21.6251184
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\left(-1-\sqrt{5}-\sqrt{2}\right)^{2}
Subtract 4 from 3 to get -1.
2\sqrt{2}\sqrt{5}+\left(\sqrt{2}\right)^{2}+\left(\sqrt{5}\right)^{2}+2\sqrt{2}+2\sqrt{5}+1
Square -1-\sqrt{5}-\sqrt{2}.
2\sqrt{10}+\left(\sqrt{2}\right)^{2}+\left(\sqrt{5}\right)^{2}+2\sqrt{2}+2\sqrt{5}+1
To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.
2\sqrt{10}+2+\left(\sqrt{5}\right)^{2}+2\sqrt{2}+2\sqrt{5}+1
The square of \sqrt{2} is 2.
2\sqrt{10}+2+5+2\sqrt{2}+2\sqrt{5}+1
The square of \sqrt{5} is 5.
2\sqrt{10}+7+2\sqrt{2}+2\sqrt{5}+1
Add 2 and 5 to get 7.
2\sqrt{10}+8+2\sqrt{2}+2\sqrt{5}
Add 7 and 1 to get 8.
\left(-1-\sqrt{5}-\sqrt{2}\right)^{2}
Subtract 4 from 3 to get -1.
2\sqrt{2}\sqrt{5}+\left(\sqrt{2}\right)^{2}+\left(\sqrt{5}\right)^{2}+2\sqrt{2}+2\sqrt{5}+1
Square -1-\sqrt{5}-\sqrt{2}.
2\sqrt{10}+\left(\sqrt{2}\right)^{2}+\left(\sqrt{5}\right)^{2}+2\sqrt{2}+2\sqrt{5}+1
To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.
2\sqrt{10}+2+\left(\sqrt{5}\right)^{2}+2\sqrt{2}+2\sqrt{5}+1
The square of \sqrt{2} is 2.
2\sqrt{10}+2+5+2\sqrt{2}+2\sqrt{5}+1
The square of \sqrt{5} is 5.
2\sqrt{10}+7+2\sqrt{2}+2\sqrt{5}+1
Add 2 and 5 to get 7.
2\sqrt{10}+8+2\sqrt{2}+2\sqrt{5}
Add 7 and 1 to get 8.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
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}