Evaluate
6\left(\sqrt{5}-5\sqrt{3}\right)\approx -38.545116362
Factor
6 {(\sqrt{5} - 5 \sqrt{3})} = -38.545116362
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6\sqrt{5}-2\times 3\sqrt{5}\sqrt{5}\sqrt{3}
Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.
6\sqrt{5}-2\times 3\times 5\sqrt{3}
Multiply \sqrt{5} and \sqrt{5} to get 5.
6\sqrt{5}-6\times 5\sqrt{3}
Multiply 2 and 3 to get 6.
6\sqrt{5}-30\sqrt{3}
Multiply 6 and 5 to get 30.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}