Which is the greatest among √2, 3√4 and 4√3?

1.	Which is the greatest among √2, 3√4 and 4√3?
Answer» Answer: 2–√,4–√3,3–√42,43,34 = 212,413,314212,413,314 = 2612,4412,33122612,4412,3312 [MAKING all the POWERS as LIKE TERMS] = 26−−√12,44−−√12,33−−√122612,4412,3312 = 64−−√12,256−−−√12,27−−√126412,25612,2712 Here 256−−−√1225612 is GREATER. Therefore, 4–√343 is greater.

Answer»

Answer:

2–√,4–√3,3–√42,43,34

= 212,413,314212,413,314

= 2612,4412,33122612,4412,3312 [MAKING all the POWERS as LIKE TERMS]

= 26−−√12,44−−√12,33−−√122612,4412,3312

= 64−−√12,256−−−√12,27−−√126412,25612,2712

Here 256−−−√1225612 is GREATER.

Therefore, 4–√343 is greater.

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