Evaluate
\sqrt{5}\approx 2.236067977
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3\sqrt{5}+3\sqrt{20}-8\sqrt{5}
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\times 2\sqrt{5}-8\sqrt{5}
Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.
3\sqrt{5}+6\sqrt{5}-8\sqrt{5}
Multiply 3 and 2 to get 6.
9\sqrt{5}-8\sqrt{5}
Combine 3\sqrt{5} and 6\sqrt{5} to get 9\sqrt{5}.
\sqrt{5}
Combine 9\sqrt{5} and -8\sqrt{5} to get \sqrt{5}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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\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
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