Evaluate
\frac{\sqrt{3}+7}{23}\approx 0.379654383
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\frac{2\left(7+\sqrt{3}\right)}{\left(7-\sqrt{3}\right)\left(7+\sqrt{3}\right)}
Rationalize the denominator of \frac{2}{7-\sqrt{3}} by multiplying numerator and denominator by 7+\sqrt{3}.
\frac{2\left(7+\sqrt{3}\right)}{7^{2}-\left(\sqrt{3}\right)^{2}}
Consider \left(7-\sqrt{3}\right)\left(7+\sqrt{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(7+\sqrt{3}\right)}{49-3}
Square 7. Square \sqrt{3}.
\frac{2\left(7+\sqrt{3}\right)}{46}
Subtract 3 from 49 to get 46.
\frac{1}{23}\left(7+\sqrt{3}\right)
Divide 2\left(7+\sqrt{3}\right) by 46 to get \frac{1}{23}\left(7+\sqrt{3}\right).
\frac{1}{23}\times 7+\frac{1}{23}\sqrt{3}
Use the distributive property to multiply \frac{1}{23} by 7+\sqrt{3}.
\frac{7}{23}+\frac{1}{23}\sqrt{3}
Multiply \frac{1}{23} and 7 to get \frac{7}{23}.
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