Evaluate
2\left(\sqrt{10}-3\right)\approx 0.32455532
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\frac{2\left(\sqrt{10}-3\right)}{\left(\sqrt{10}+3\right)\left(\sqrt{10}-3\right)}
Rationalize the denominator of \frac{2}{\sqrt{10}+3} by multiplying numerator and denominator by \sqrt{10}-3.
\frac{2\left(\sqrt{10}-3\right)}{\left(\sqrt{10}\right)^{2}-3^{2}}
Consider \left(\sqrt{10}+3\right)\left(\sqrt{10}-3\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{10}-3\right)}{10-9}
Square \sqrt{10}. Square 3.
\frac{2\left(\sqrt{10}-3\right)}{1}
Subtract 9 from 10 to get 1.
2\left(\sqrt{10}-3\right)
Anything divided by one gives itself.
2\sqrt{10}-6
Use the distributive property to multiply 2 by \sqrt{10}-3.
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