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Which of the following numbers are greater than 6 and less than 8? Explainhow you know.

Which of the following numbers are greater than 6 and less than 8? Explainhow you-example-1

1 Answer

4 votes

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,


64<80
\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


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

and


6>3>\sqrt[]{7}

thus


6>\sqrt[]{7}

Now


36<60
\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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