arrange in ascending order of magnitude:- 4√10,3√6,√3
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Let us rewrite the given set of magnitudes
3
2
,
6
3
,
9
4
as follows:
3
2
=(2)
3
1
6
3
=(3)
6
1
9
4
=(4)
9
1
We now take the LCM of the denominators of the powers to make the denominators same, then the above magnitudes will be:
3
2
=(2)
3×6
1×6
=(2)
18
6
=(2
6
)
18
1
=(64)
18
1
=
18
64
6
3
=(3)
6×3
1×3
=(3)
18
3
=(3
3
)
18
1
=(27)
18
1
=
18
27
9
4
=(4)
9×2
1×2
=(4)
18
2
=(4
2
)
18
1
=(16)
18
1
=
18
16
Therefore, the descending order is shown below:
18
64
>
18
27
>
18
16
⇒
3
2
>
6
3
>
9
4
Hence, the descending order of the magnitude
3
2
,
6
3
,
9
4
is
3
2
>
6
3
>
9
4
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