Question

Which is greater ? 
⁴√4 or ⁵√5
​

Answer 1

SOLUTION:-

The above two surds have different orders. The are 4 and 5.

Using the least common multiple of the orders 4 and 5, we can convert them into surds of same order. 

Least common multiple of (4 and 5) is 20.

Then, 

⁴√4  =  ⁴×⁵√(45)  =  ²⁰√1024

⁵√5  =  ⁵×⁴√(5⁴)  =  ²⁰√625

Now, the given two surds are expressed in the same order. 

Compare the radicands :

1024  >  625

Then, 

²⁰√1024  >  ²⁰√625

Therefore, 

⁴√4  >  ⁵√5