Evaluate
47-2\sqrt{442}\approx 4.952407917
Expand
47-2\sqrt{442}
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\left(\sqrt{34}\right)^{2}-2\sqrt{34}\sqrt{13}+\left(\sqrt{13}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{34}-\sqrt{13}\right)^{2}.
34-2\sqrt{34}\sqrt{13}+\left(\sqrt{13}\right)^{2}
The square of \sqrt{34} is 34.
34-2\sqrt{442}+\left(\sqrt{13}\right)^{2}
To multiply \sqrt{34} and \sqrt{13}, multiply the numbers under the square root.
34-2\sqrt{442}+13
The square of \sqrt{13} is 13.
47-2\sqrt{442}
Add 34 and 13 to get 47.
\left(\sqrt{34}\right)^{2}-2\sqrt{34}\sqrt{13}+\left(\sqrt{13}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{34}-\sqrt{13}\right)^{2}.
34-2\sqrt{34}\sqrt{13}+\left(\sqrt{13}\right)^{2}
The square of \sqrt{34} is 34.
34-2\sqrt{442}+\left(\sqrt{13}\right)^{2}
To multiply \sqrt{34} and \sqrt{13}, multiply the numbers under the square root.
34-2\sqrt{442}+13
The square of \sqrt{13} is 13.
47-2\sqrt{442}
Add 34 and 13 to get 47.
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