Evaluate
4\sqrt{10}+22\approx 34.649110641
Expand
4 \sqrt{10} + 22 = 34.649110641
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\left(\sqrt{2}\right)^{2}+4\sqrt{2}\sqrt{5}+4\left(\sqrt{5}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{2}+2\sqrt{5}\right)^{2}.
2+4\sqrt{2}\sqrt{5}+4\left(\sqrt{5}\right)^{2}
The square of \sqrt{2} is 2.
2+4\sqrt{10}+4\left(\sqrt{5}\right)^{2}
To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.
2+4\sqrt{10}+4\times 5
The square of \sqrt{5} is 5.
2+4\sqrt{10}+20
Multiply 4 and 5 to get 20.
22+4\sqrt{10}
Add 2 and 20 to get 22.
\left(\sqrt{2}\right)^{2}+4\sqrt{2}\sqrt{5}+4\left(\sqrt{5}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{2}+2\sqrt{5}\right)^{2}.
2+4\sqrt{2}\sqrt{5}+4\left(\sqrt{5}\right)^{2}
The square of \sqrt{2} is 2.
2+4\sqrt{10}+4\left(\sqrt{5}\right)^{2}
To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.
2+4\sqrt{10}+4\times 5
The square of \sqrt{5} is 5.
2+4\sqrt{10}+20
Multiply 4 and 5 to get 20.
22+4\sqrt{10}
Add 2 and 20 to get 22.
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}