Evaluate
125
Factor
5^{3}
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3^{2}\left(\sqrt{5}\right)^{2}+\left(4\sqrt{5}\right)^{2}
Expand \left(3\sqrt{5}\right)^{2}.
9\left(\sqrt{5}\right)^{2}+\left(4\sqrt{5}\right)^{2}
Calculate 3 to the power of 2 and get 9.
9\times 5+\left(4\sqrt{5}\right)^{2}
The square of \sqrt{5} is 5.
45+\left(4\sqrt{5}\right)^{2}
Multiply 9 and 5 to get 45.
45+4^{2}\left(\sqrt{5}\right)^{2}
Expand \left(4\sqrt{5}\right)^{2}.
45+16\left(\sqrt{5}\right)^{2}
Calculate 4 to the power of 2 and get 16.
45+16\times 5
The square of \sqrt{5} is 5.
45+80
Multiply 16 and 5 to get 80.
125
Add 45 and 80 to get 125.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}