Evaluate
\frac{3\sqrt{30}}{20}\approx 0.821583836
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\sqrt{\frac{54}{80}}
Expand \frac{5.4}{8} by multiplying both numerator and the denominator by 10.
\sqrt{\frac{27}{40}}
Reduce the fraction \frac{54}{80} to lowest terms by extracting and canceling out 2.
\frac{\sqrt{27}}{\sqrt{40}}
Rewrite the square root of the division \sqrt{\frac{27}{40}} as the division of square roots \frac{\sqrt{27}}{\sqrt{40}}.
\frac{3\sqrt{3}}{\sqrt{40}}
Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.
\frac{3\sqrt{3}}{2\sqrt{10}}
Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.
\frac{3\sqrt{3}\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}
Rationalize the denominator of \frac{3\sqrt{3}}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.
\frac{3\sqrt{3}\sqrt{10}}{2\times 10}
The square of \sqrt{10} is 10.
\frac{3\sqrt{30}}{2\times 10}
To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.
\frac{3\sqrt{30}}{20}
Multiply 2 and 10 to get 20.
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Matrix
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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}