Question

Write in descending order: 2^(1/2) , 4^(1/3), 3^(1/4)​

Answer 1

4(1/3), 2(1/2),3(1/4)

Explanation:

2^1/2 equals the root of 2 and equals 1.4…

4^(1/3) equals 1.6

3^(1/4) equals 1.3

Answer 2

• See below

Explanation:

We cant equalize the bases but we can make the powers same.

It will let us estimate better:

• 
  `2^(1/2) = (2^6)^(1/12) = 64^(1/12)`
• 
  `4^(1/3)=(4^4)^(1/12) = 256^(1/12)`
• 
  `3^(1/4)=(3^3)^(1/12)= 27^(1/12)`

Now it is easy to compare, the smaller the base the smaller the number:

• 
  `27^(1/12)<64^(1/12)<256^(1/12)` or
• 
  `3^(1/4)<2^(1/2)<4^(1/3)`