Evaluate
6\left(\sqrt{5}+2\sqrt{10}\right)\approx 51.363739787
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12\sqrt{10}+3\sqrt{10}\sqrt{2}
Use the distributive property to multiply 3\sqrt{10} by 4+\sqrt{2}.
12\sqrt{10}+3\sqrt{2}\sqrt{5}\sqrt{2}
Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.
12\sqrt{10}+3\times 2\sqrt{5}
Multiply \sqrt{2} and \sqrt{2} to get 2.
12\sqrt{10}+6\sqrt{5}
Multiply 3 and 2 to get 6.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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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}