Question

arrange the surd please​

Answer 1

Step-by-step explanation:

Given :-

√2 , ³√4 and ⁴√7

To find :-

Arrange them in order ?

Solution :-

Given surds are √2 , ³√4 and ⁴√7

√2 can be written as 2½

³√4 can be written as 4⅓

⁴√7 can be written as 7¼

The powers are 1/2 , 1/3 and 1/4

The denominators are 2 , 3 and 4

LCM of 2 , 3 and 4 = 12

So, √2

= 2½

= [(2)½]⁶/⁶

=> 2⁶/¹²

=> ¹²√2⁶

=> ¹²√64

³√4

=> 4⅓

=> (4⅓)⁴/⁴

=> 4⁴/¹²

=> ¹²√4⁴

=> ¹²√256

and

⁴√7

=> 7¼

=> (7¼)³/³

=> 7³/¹²

=> ¹²√7³

=> ¹²√343

Now The above surds becomes

¹²√64, ¹²√256 and ¹²√343

Ascending order = ¹²√64, ¹²√256 and ¹²√343

Descending order = ¹²√343,¹²√256 and ¹²√64