Evaluate
3\left(\sqrt{7}+2\right)\approx 13.937253933
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\frac{9\left(\sqrt{7}+2\right)}{\left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right)}
Rationalize the denominator of \frac{9}{\sqrt{7}-2} by multiplying numerator and denominator by \sqrt{7}+2.
\frac{9\left(\sqrt{7}+2\right)}{\left(\sqrt{7}\right)^{2}-2^{2}}
Consider \left(\sqrt{7}-2\right)\left(\sqrt{7}+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{9\left(\sqrt{7}+2\right)}{7-4}
Square \sqrt{7}. Square 2.
\frac{9\left(\sqrt{7}+2\right)}{3}
Subtract 4 from 7 to get 3.
3\left(\sqrt{7}+2\right)
Divide 9\left(\sqrt{7}+2\right) by 3 to get 3\left(\sqrt{7}+2\right).
3\sqrt{7}+6
Use the distributive property to multiply 3 by \sqrt{7}+2.
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