Evaluate
\frac{3\sqrt{5}}{2}\approx 3.354101966
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\sqrt{\frac{25}{4}+5}
Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.
\sqrt{\frac{25}{4}+\frac{20}{4}}
Convert 5 to fraction \frac{20}{4}.
\sqrt{\frac{25+20}{4}}
Since \frac{25}{4} and \frac{20}{4} have the same denominator, add them by adding their numerators.
\sqrt{\frac{45}{4}}
Add 25 and 20 to get 45.
\frac{\sqrt{45}}{\sqrt{4}}
Rewrite the square root of the division \sqrt{\frac{45}{4}} as the division of square roots \frac{\sqrt{45}}{\sqrt{4}}.
\frac{3\sqrt{5}}{\sqrt{4}}
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}.
\frac{3\sqrt{5}}{2}
Calculate the square root of 4 and get 2.
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}