Evaluate
\sqrt{30}\approx 5.477225575
Share
Copied to clipboard
\frac{5\sqrt{18}}{\sqrt{15}}
Calculate the square root of 25 and get 5.
\frac{5\times 3\sqrt{2}}{\sqrt{15}}
Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.
\frac{15\sqrt{2}}{\sqrt{15}}
Multiply 5 and 3 to get 15.
\frac{15\sqrt{2}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}
Rationalize the denominator of \frac{15\sqrt{2}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.
\frac{15\sqrt{2}\sqrt{15}}{15}
The square of \sqrt{15} is 15.
\frac{15\sqrt{30}}{15}
To multiply \sqrt{2} and \sqrt{15}, multiply the numbers under the square root.
\sqrt{30}
Cancel out 15 and 15.
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}