Evaluate
\sqrt{10}-3\approx 0.16227766
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\frac{1}{\sqrt{10}+3}
Calculate the square root of 9 and get 3.
\frac{\sqrt{10}-3}{\left(\sqrt{10}+3\right)\left(\sqrt{10}-3\right)}
Rationalize the denominator of \frac{1}{\sqrt{10}+3} by multiplying numerator and denominator by \sqrt{10}-3.
\frac{\sqrt{10}-3}{\left(\sqrt{10}\right)^{2}-3^{2}}
Consider \left(\sqrt{10}+3\right)\left(\sqrt{10}-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{\sqrt{10}-3}{10-9}
Square \sqrt{10}. Square 3.
\frac{\sqrt{10}-3}{1}
Subtract 9 from 10 to get 1.
\sqrt{10}-3
Anything divided by one gives itself.
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Limits
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