Evaluate
\sqrt{5}\approx 2.236067977
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3\sqrt{5}-\frac{10}{\sqrt{5}}
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}.
3\sqrt{5}-\frac{10\sqrt{5}}{\left(\sqrt{5}\right)^{2}}
Rationalize the denominator of \frac{10}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
3\sqrt{5}-\frac{10\sqrt{5}}{5}
The square of \sqrt{5} is 5.
3\sqrt{5}-2\sqrt{5}
Divide 10\sqrt{5} by 5 to get 2\sqrt{5}.
\sqrt{5}
Combine 3\sqrt{5} and -2\sqrt{5} to get \sqrt{5}.
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}