Evaluate
5\left(\sqrt{3}-1\right)\approx 3.660254038
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\frac{10\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}
Rationalize the denominator of \frac{10}{\sqrt{3}+1} by multiplying numerator and denominator by \sqrt{3}-1.
\frac{10\left(\sqrt{3}-1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}
Consider \left(\sqrt{3}+1\right)\left(\sqrt{3}-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{10\left(\sqrt{3}-1\right)}{3-1}
Square \sqrt{3}. Square 1.
\frac{10\left(\sqrt{3}-1\right)}{2}
Subtract 1 from 3 to get 2.
5\left(\sqrt{3}-1\right)
Divide 10\left(\sqrt{3}-1\right) by 2 to get 5\left(\sqrt{3}-1\right).
5\sqrt{3}-5
Use the distributive property to multiply 5 by \sqrt{3}-1.
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