Evaluate
\sqrt{5}\approx 2.236067977
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\frac{3}{5}\times \frac{\sqrt{125}}{\sqrt{9}}
Rewrite the square root of the division \sqrt{\frac{125}{9}} as the division of square roots \frac{\sqrt{125}}{\sqrt{9}}.
\frac{3}{5}\times \frac{5\sqrt{5}}{\sqrt{9}}
Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.
\frac{3}{5}\times \frac{5\sqrt{5}}{3}
Calculate the square root of 9 and get 3.
\frac{3\times 5\sqrt{5}}{5\times 3}
Multiply \frac{3}{5} times \frac{5\sqrt{5}}{3} by multiplying numerator times numerator and denominator times denominator.
\sqrt{5}
Cancel out 3\times 5 in both numerator and denominator.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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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}