Evaluate
\sqrt{2}+8\sqrt{5}\approx 19.302757382
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3\sqrt{5}+\sqrt{18}-\sqrt{8}+\sqrt{125}
Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.
3\sqrt{5}+3\sqrt{2}-\sqrt{8}+\sqrt{125}
Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.
3\sqrt{5}+3\sqrt{2}-2\sqrt{2}+\sqrt{125}
Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.
3\sqrt{5}+\sqrt{2}+\sqrt{125}
Combine 3\sqrt{2} and -2\sqrt{2} to get \sqrt{2}.
3\sqrt{5}+\sqrt{2}+5\sqrt{5}
Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.
8\sqrt{5}+\sqrt{2}
Combine 3\sqrt{5} and 5\sqrt{5} to get 8\sqrt{5}.
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y = 3x + 4
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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
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