Evaluate
\frac{3\sqrt{7}}{5}+\sqrt{10}-2\sqrt{3}\approx 1.285626832
Factor
\frac{3 \sqrt{7} + 5 \sqrt{10} - 10 \sqrt{3}}{5} = 1.28562683166938
Share
Copied to clipboard
\frac{3\sqrt{7}}{5}-2\sqrt{3}+\sqrt{10}
Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.
\frac{3\sqrt{7}}{5}+\frac{5\left(-2\sqrt{3}+\sqrt{10}\right)}{5}
To add or subtract expressions, expand them to make their denominators the same. Multiply -2\sqrt{3}+\sqrt{10} times \frac{5}{5}.
\frac{3\sqrt{7}+5\left(-2\sqrt{3}+\sqrt{10}\right)}{5}
Since \frac{3\sqrt{7}}{5} and \frac{5\left(-2\sqrt{3}+\sqrt{10}\right)}{5} have the same denominator, add them by adding their numerators.
\frac{3\sqrt{7}-10\sqrt{3}+5\sqrt{10}}{5}
Do the multiplications in 3\sqrt{7}+5\left(-2\sqrt{3}+\sqrt{10}\right).
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}