Evaluate
\sqrt{6}\approx 2.449489743
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\frac{1}{2}\sqrt{4+0-4\left(-5\right)}
Calculate -2 to the power of 2 and get 4.
\frac{1}{2}\sqrt{4-4\left(-5\right)}
Add 4 and 0 to get 4.
\frac{1}{2}\sqrt{4-\left(-20\right)}
Multiply 4 and -5 to get -20.
\frac{1}{2}\sqrt{4+20}
The opposite of -20 is 20.
\frac{1}{2}\sqrt{24}
Add 4 and 20 to get 24.
\frac{1}{2}\times 2\sqrt{6}
Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.
\sqrt{6}
Cancel out 2 and 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}