Evaluate
\sqrt{17}-4\approx 0.123105626
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\frac{4-\sqrt{17}}{\left(4+\sqrt{17}\right)\left(4-\sqrt{17}\right)}
Rationalize the denominator of \frac{1}{4+\sqrt{17}} by multiplying numerator and denominator by 4-\sqrt{17}.
\frac{4-\sqrt{17}}{4^{2}-\left(\sqrt{17}\right)^{2}}
Consider \left(4+\sqrt{17}\right)\left(4-\sqrt{17}\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{4-\sqrt{17}}{16-17}
Square 4. Square \sqrt{17}.
\frac{4-\sqrt{17}}{-1}
Subtract 17 from 16 to get -1.
-4-\left(-\sqrt{17}\right)
Anything divided by -1 gives its opposite. To find the opposite of 4-\sqrt{17}, find the opposite of each term.
-4+\sqrt{17}
The opposite of -\sqrt{17} is \sqrt{17}.
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Limits
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