Question

Order the real numbers from greatest (top) to least (bottom)

Answer 1

`√(102) > 6(1)/(2) > \sqrt[(1)/(3)]{102} > (69)/(25)`

Explanation:

`4 < \sqrt[3]{102} < 5`
`\left\{√(64)=4,\sqrt[7]{125}=5\right\}`

`6(1)/(2)=6.5`

`(69)/(25)=2.76`

`10 < √(102) < 11`
`\left\{√(100)=10√(121)=11\right\}`

So from greater to least:

`√(102) > 6(1)/(2) > \sqrt[(1)/(3)]{102} > (69)/(25)`

I hope this helps you

:)

Answer 2

`\sqrt[3]{102} = 4.672\\6.5\\(69)/(25) =2.76\\√(102) = 10.0995`

Thus the numbers from greatest to least is

`√(102), 6(1)/(2) ,\sqrt[3]{102} , (69)/(25)`

Hope that helps!