Question

asked Nov 2, 2023 154k views

1 Answer

Sammers · Answer 1 · 2023-11-08T06:35:43+0000

Let's analyze each case and see if they are less than 8 first:

$7<8,therefore(7)^{(1)/(2)}<8$
$\sqrt[]{64}=8$

thus

$\sqrt[]{60}<\sqrt[]{64}=8$
$\sqrt[]{60}<8$

Finally,

$\sqrt[]{64}<\sqrt[]{80}$

thus

$8<\sqrt[]{80}$

In sumary, the first two options are less than 8, but not the third.

Now let's see if they are greater than 6

$\sqrt[]{9}>\sqrt[]{7}$
$3>\sqrt[]{7}$

and

$6>3>\sqrt[]{7}$

thus

$6>\sqrt[]{7}$

Now

$\sqrt[]{36}<\sqrt[]{60}$

and so

$6<\sqrt[]{60}$

Finally

$\sqrt[]{80}>\sqrt[]{60}>6$

thus

$\sqrt[]{80}>6$

In conclussion, the second and third options are greater than 6, but not the first.

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