Evaluate
2^{\frac{5}{2}}-6\approx -0.343145751
Factor
2 {(2 \sqrt{2} - 3)} = -0.343145751
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2-2\sqrt{2}\left(-2+2\sqrt{2}\right)
The opposite of -2 is 2.
2+4\sqrt{2}-4\left(\sqrt{2}\right)^{2}
Use the distributive property to multiply -2\sqrt{2} by -2+2\sqrt{2}.
2+4\sqrt{2}-4\times 2
The square of \sqrt{2} is 2.
2+4\sqrt{2}-8
Multiply -4 and 2 to get -8.
-6+4\sqrt{2}
Subtract 8 from 2 to get -6.
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}