Evaluate
2\left(\sqrt{35}+6\right)\approx 23.832159566
Expand
2 \sqrt{35} + 12 = 23.832159566
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\left(\sqrt{7}\right)^{2}+2\sqrt{7}\sqrt{5}+\left(\sqrt{5}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{7}+\sqrt{5}\right)^{2}.
7+2\sqrt{7}\sqrt{5}+\left(\sqrt{5}\right)^{2}
The square of \sqrt{7} is 7.
7+2\sqrt{35}+\left(\sqrt{5}\right)^{2}
To multiply \sqrt{7} and \sqrt{5}, multiply the numbers under the square root.
7+2\sqrt{35}+5
The square of \sqrt{5} is 5.
12+2\sqrt{35}
Add 7 and 5 to get 12.
\left(\sqrt{7}\right)^{2}+2\sqrt{7}\sqrt{5}+\left(\sqrt{5}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{7}+\sqrt{5}\right)^{2}.
7+2\sqrt{7}\sqrt{5}+\left(\sqrt{5}\right)^{2}
The square of \sqrt{7} is 7.
7+2\sqrt{35}+\left(\sqrt{5}\right)^{2}
To multiply \sqrt{7} and \sqrt{5}, multiply the numbers under the square root.
7+2\sqrt{35}+5
The square of \sqrt{5} is 5.
12+2\sqrt{35}
Add 7 and 5 to get 12.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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Matrix
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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}