Evaluate
70-30\sqrt{5}\approx 2.917960675
Expand
70-30\sqrt{5}
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25-30\sqrt{5}+9\left(\sqrt{5}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5-3\sqrt{5}\right)^{2}.
25-30\sqrt{5}+9\times 5
The square of \sqrt{5} is 5.
25-30\sqrt{5}+45
Multiply 9 and 5 to get 45.
70-30\sqrt{5}
Add 25 and 45 to get 70.
25-30\sqrt{5}+9\left(\sqrt{5}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5-3\sqrt{5}\right)^{2}.
25-30\sqrt{5}+9\times 5
The square of \sqrt{5} is 5.
25-30\sqrt{5}+45
Multiply 9 and 5 to get 45.
70-30\sqrt{5}
Add 25 and 45 to get 70.
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Limits
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