Evaluate
\sqrt{5}+\frac{43}{66}\approx 2.887583129
Factor
\frac{66 \sqrt{5} + 43}{66} = 2.887583129014941
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\frac{1}{2}+\frac{5}{33}+\sqrt{5}
Reduce the fraction \frac{15}{99} to lowest terms by extracting and canceling out 3.
\frac{33}{66}+\frac{10}{66}+\sqrt{5}
Least common multiple of 2 and 33 is 66. Convert \frac{1}{2} and \frac{5}{33} to fractions with denominator 66.
\frac{33+10}{66}+\sqrt{5}
Since \frac{33}{66} and \frac{10}{66} have the same denominator, add them by adding their numerators.
\frac{43}{66}+\sqrt{5}
Add 33 and 10 to get 43.
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}