Evaluate
2\left(\sqrt{21}+5\right)\approx 19.16515139
Expand
2 \sqrt{21} + 10 = 19.16515139
Share
Copied to clipboard
\left(\sqrt{3}\right)^{2}+2\sqrt{3}\sqrt{7}+\left(\sqrt{7}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{3}+\sqrt{7}\right)^{2}.
3+2\sqrt{3}\sqrt{7}+\left(\sqrt{7}\right)^{2}
The square of \sqrt{3} is 3.
3+2\sqrt{21}+\left(\sqrt{7}\right)^{2}
To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.
3+2\sqrt{21}+7
The square of \sqrt{7} is 7.
10+2\sqrt{21}
Add 3 and 7 to get 10.
\left(\sqrt{3}\right)^{2}+2\sqrt{3}\sqrt{7}+\left(\sqrt{7}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{3}+\sqrt{7}\right)^{2}.
3+2\sqrt{3}\sqrt{7}+\left(\sqrt{7}\right)^{2}
The square of \sqrt{3} is 3.
3+2\sqrt{21}+\left(\sqrt{7}\right)^{2}
To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.
3+2\sqrt{21}+7
The square of \sqrt{7} is 7.
10+2\sqrt{21}
Add 3 and 7 to get 10.
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}