Evaluate
2\sqrt{3}\approx 3.464101615
Share
Copied to clipboard
\frac{6\times \frac{\sqrt{5}}{\sqrt{3}}-10\sqrt{\frac{3}{5}}+2\sqrt{15}}{\sqrt{5}}
Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.
\frac{6\times \frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-10\sqrt{\frac{3}{5}}+2\sqrt{15}}{\sqrt{5}}
Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
\frac{6\times \frac{\sqrt{5}\sqrt{3}}{3}-10\sqrt{\frac{3}{5}}+2\sqrt{15}}{\sqrt{5}}
The square of \sqrt{3} is 3.
\frac{6\times \frac{\sqrt{15}}{3}-10\sqrt{\frac{3}{5}}+2\sqrt{15}}{\sqrt{5}}
To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.
\frac{2\sqrt{15}-10\sqrt{\frac{3}{5}}+2\sqrt{15}}{\sqrt{5}}
Cancel out 3, the greatest common factor in 6 and 3.
\frac{2\sqrt{15}-10\times \frac{\sqrt{3}}{\sqrt{5}}+2\sqrt{15}}{\sqrt{5}}
Rewrite the square root of the division \sqrt{\frac{3}{5}} as the division of square roots \frac{\sqrt{3}}{\sqrt{5}}.
\frac{2\sqrt{15}-10\times \frac{\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+2\sqrt{15}}{\sqrt{5}}
Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
\frac{2\sqrt{15}-10\times \frac{\sqrt{3}\sqrt{5}}{5}+2\sqrt{15}}{\sqrt{5}}
The square of \sqrt{5} is 5.
\frac{2\sqrt{15}-10\times \frac{\sqrt{15}}{5}+2\sqrt{15}}{\sqrt{5}}
To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.
\frac{2\sqrt{15}-2\sqrt{15}+2\sqrt{15}}{\sqrt{5}}
Cancel out 5, the greatest common factor in 10 and 5.
\frac{2\sqrt{15}}{\sqrt{5}}
Combine 2\sqrt{15} and -2\sqrt{15} to get 0.
\frac{2\sqrt{15}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}
Rationalize the denominator of \frac{2\sqrt{15}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
\frac{2\sqrt{15}\sqrt{5}}{5}
The square of \sqrt{5} is 5.
\frac{2\sqrt{5}\sqrt{3}\sqrt{5}}{5}
Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.
\frac{2\times 5\sqrt{3}}{5}
Multiply \sqrt{5} and \sqrt{5} to get 5.
2\sqrt{3}
Cancel out 5 and 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}