Evaluate
3\left(\sqrt{7}-1\right)\approx 4.937253933
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\frac{18\left(\sqrt{7}-1\right)}{\left(\sqrt{7}+1\right)\left(\sqrt{7}-1\right)}
Rationalize the denominator of \frac{18}{\sqrt{7}+1} by multiplying numerator and denominator by \sqrt{7}-1.
\frac{18\left(\sqrt{7}-1\right)}{\left(\sqrt{7}\right)^{2}-1^{2}}
Consider \left(\sqrt{7}+1\right)\left(\sqrt{7}-1\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{18\left(\sqrt{7}-1\right)}{7-1}
Square \sqrt{7}. Square 1.
\frac{18\left(\sqrt{7}-1\right)}{6}
Subtract 1 from 7 to get 6.
3\left(\sqrt{7}-1\right)
Divide 18\left(\sqrt{7}-1\right) by 6 to get 3\left(\sqrt{7}-1\right).
3\sqrt{7}-3
Use the distributive property to multiply 3 by \sqrt{7}-1.
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