Evaluate
\frac{3\left(\sqrt{2}+7\right)}{47}\approx 0.537077461
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\frac{3\left(7+\sqrt{2}\right)}{\left(7-\sqrt{2}\right)\left(7+\sqrt{2}\right)}
Rationalize the denominator of \frac{3}{7-\sqrt{2}} by multiplying numerator and denominator by 7+\sqrt{2}.
\frac{3\left(7+\sqrt{2}\right)}{7^{2}-\left(\sqrt{2}\right)^{2}}
Consider \left(7-\sqrt{2}\right)\left(7+\sqrt{2}\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{3\left(7+\sqrt{2}\right)}{49-2}
Square 7. Square \sqrt{2}.
\frac{3\left(7+\sqrt{2}\right)}{47}
Subtract 2 from 49 to get 47.
\frac{21+3\sqrt{2}}{47}
Use the distributive property to multiply 3 by 7+\sqrt{2}.
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