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42 votes
42 votes
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User Dan Garland
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1 Answer

20 votes
20 votes

Let's simplify each expression

1.


\frac{10\pi\sqrt[]{2}-8\pi\sqrt[]{2}}{2\sqrt[]{2}}=\frac{(10-8)\pi\sqrt[]{2}}{2\sqrt[]{2}}=(2\pi)/(2)=\pi

2.


\frac{\sqrt[]{24}-\sqrt[]{54}}{\sqrt[]{6}}=\frac{\sqrt[]{6\cdot4}-\sqrt[]{6\cdot9}}{\sqrt[]{6}}=\frac{2\sqrt[]{6}-3\sqrt[]{6}}{\sqrt[]{6}}=\frac{(2-3)\sqrt[]{6}}{\sqrt[]{6}}=-1

3.


\pi\sqrt[]{(3)/(5)}\cdot\pi\sqrt[]{(5)/(3)}=\pi^2\sqrt[]{(3)/(5)\cdot(5)/(3)}=\pi^2\sqrt[]{1}=\pi^2

Using the results above, we can say that the right order is


\frac{\sqrt[]{24}-\sqrt[]{54}}{\sqrt[]{6}}<\frac{10\pi\sqrt[]{2}-8\pi\sqrt[]{2}}{2\sqrt[]{2}}<\pi\sqrt[]{(3)/(5)}\cdot\pi\sqrt[]{(5)/(3)}

User MandisaW
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