Evaluate
34-24\sqrt{2}\approx 0.058874503
Expand
34-24\sqrt{2}
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9\left(\sqrt{2}\right)^{2}-24\sqrt{2}+16
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3\sqrt{2}-4\right)^{2}.
9\times 2-24\sqrt{2}+16
The square of \sqrt{2} is 2.
18-24\sqrt{2}+16
Multiply 9 and 2 to get 18.
34-24\sqrt{2}
Add 18 and 16 to get 34.
9\left(\sqrt{2}\right)^{2}-24\sqrt{2}+16
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3\sqrt{2}-4\right)^{2}.
9\times 2-24\sqrt{2}+16
The square of \sqrt{2} is 2.
18-24\sqrt{2}+16
Multiply 9 and 2 to get 18.
34-24\sqrt{2}
Add 18 and 16 to get 34.
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