Evaluate
\frac{12\sqrt{21}}{7}\approx 7.855844048
Share
Copied to clipboard
\frac{\sqrt{432}}{\sqrt{7}}
Rewrite the square root of the division \sqrt{\frac{432}{7}} as the division of square roots \frac{\sqrt{432}}{\sqrt{7}}.
\frac{12\sqrt{3}}{\sqrt{7}}
Factor 432=12^{2}\times 3. Rewrite the square root of the product \sqrt{12^{2}\times 3} as the product of square roots \sqrt{12^{2}}\sqrt{3}. Take the square root of 12^{2}.
\frac{12\sqrt{3}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}
Rationalize the denominator of \frac{12\sqrt{3}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.
\frac{12\sqrt{3}\sqrt{7}}{7}
The square of \sqrt{7} is 7.
\frac{12\sqrt{21}}{7}
To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.
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}