Question

If you answer my question I'll give you a cookie also I'll give you five stars

Answer 1

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)}`