Question

Question For Everyone

Express 2/3 ³√16 as Pure Surd.

No Spam
No Copy
Needed Quality Answer​

Answer 1

Answer:

2/3 × ∛16

⇒ ∛(8/27) × ∛16

⇒ ∛( 8 × 16 ) / ∛27

⇒ ∛( 128/27 )

Step-by-step explanation:

A pure surd is a surd which is fully rational .

So we are given with a mixed surd because 2/3 is not rational .

In order to make a pure surd an impure surd , we need to make the rational numbers irrational .

A mixed surd is a surd which has both rational as well as irrational parts .

Some properties of a surd is :

∛a × ∛b = ∛ab

∛a / ∛b = ∛( a/b )

Hence we can use this property to make the mixed surd a pure one .

In order to make the concept clear here is an example :

To make 4 a pure surd :

Take roots over 4 without changing the value :- √4 × √4 = √16 .

To make 2/3 pure surd :

Take square root over 2/3 :- √( 2/3 × 2/3 ) = √( 4/9 )

Answer 2

ANSWER:-----------

2/3 × 16
(8/27) × 16
( 8 × 16 ) / 27
( 128/27 )

{according to me when we will shift 2/3 inside }

{root it will become 4/9 and 18 is already there then it will become under root 8}


4 a pure surd :

{Take roots over 4 :-

{√4 × √4 = √16 .}

2/3 pure surd :

{Take square root over 2/3 :-}

{ √( 2/3 × 2/3 ) = √( 4/9 }

hope it helps:--

T!—!ANKS!!!