Evaluate
\sqrt{5}-\sqrt{3}\approx 0.50401717
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\frac{2\left(\sqrt{3}-\sqrt{5}\right)}{\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{3}-\sqrt{5}\right)}
Rationalize the denominator of \frac{2}{\sqrt{3}+\sqrt{5}} by multiplying numerator and denominator by \sqrt{3}-\sqrt{5}.
\frac{2\left(\sqrt{3}-\sqrt{5}\right)}{\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}
Consider \left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{3}-\sqrt{5}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{2\left(\sqrt{3}-\sqrt{5}\right)}{3-5}
Square \sqrt{3}. Square \sqrt{5}.
\frac{2\left(\sqrt{3}-\sqrt{5}\right)}{-2}
Subtract 5 from 3 to get -2.
-\left(\sqrt{3}-\sqrt{5}\right)
Cancel out -2 and -2.
-\sqrt{3}-\left(-\sqrt{5}\right)
To find the opposite of \sqrt{3}-\sqrt{5}, find the opposite of each term.
-\sqrt{3}+\sqrt{5}
The opposite of -\sqrt{5} is \sqrt{5}.
Examples
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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
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