Evaluate
\frac{3\left(\sqrt{5}+3\right)}{5}\approx 3.141640786
Factor
\frac{3 {(\sqrt{5} + 3)}}{5} = 3.141640786499874
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\frac{9}{5}+\frac{\sqrt{9}}{\sqrt{5}}
Rewrite the square root of the division \sqrt{\frac{9}{5}} as the division of square roots \frac{\sqrt{9}}{\sqrt{5}}.
\frac{9}{5}+\frac{3}{\sqrt{5}}
Calculate the square root of 9 and get 3.
\frac{9}{5}+\frac{3\sqrt{5}}{\left(\sqrt{5}\right)^{2}}
Rationalize the denominator of \frac{3}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
\frac{9}{5}+\frac{3\sqrt{5}}{5}
The square of \sqrt{5} is 5.
\frac{9+3\sqrt{5}}{5}
Since \frac{9}{5} and \frac{3\sqrt{5}}{5} have the same denominator, add them by adding their numerators.
Examples
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{ 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}