Evaluate
\frac{\sqrt{15}}{2}+2\approx 3.936491673
Expand
\frac{\sqrt{15}}{2} + 2 = 3.936491673
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\left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{3}\right)^{2}
Use the distributive property to multiply \frac{1}{2} by \sqrt{5}+\sqrt{3}.
\frac{1}{4}\left(\sqrt{5}\right)^{2}+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{3}\right)^{2}.
\frac{1}{4}\times 5+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}
The square of \sqrt{5} is 5.
\frac{5}{4}+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}
Multiply \frac{1}{4} and 5 to get \frac{5}{4}.
\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{1}{4}\left(\sqrt{3}\right)^{2}
To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.
\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{1}{4}\times 3
The square of \sqrt{3} is 3.
\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{3}{4}
Multiply \frac{1}{4} and 3 to get \frac{3}{4}.
2+\frac{1}{2}\sqrt{15}
Add \frac{5}{4} and \frac{3}{4} to get 2.
\left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{3}\right)^{2}
Use the distributive property to multiply \frac{1}{2} by \sqrt{5}+\sqrt{3}.
\frac{1}{4}\left(\sqrt{5}\right)^{2}+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{3}\right)^{2}.
\frac{1}{4}\times 5+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}
The square of \sqrt{5} is 5.
\frac{5}{4}+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}
Multiply \frac{1}{4} and 5 to get \frac{5}{4}.
\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{1}{4}\left(\sqrt{3}\right)^{2}
To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.
\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{1}{4}\times 3
The square of \sqrt{3} is 3.
\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{3}{4}
Multiply \frac{1}{4} and 3 to get \frac{3}{4}.
2+\frac{1}{2}\sqrt{15}
Add \frac{5}{4} and \frac{3}{4} to get 2.
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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