Question

What is the order of the surd ∛√5? Choose the correct alternative answer for the question given below.
(A) 3
(B) 2
(C) 6
(D) 5

Answer 1

Hey there !

Surd : Let n be a positive integer and a be a rational number ,

if a^1/n is not a rational number,

that is not a power of any number to exponent "n " ,

then a^1/n is called a surd of nth order .

Order of the surd a^1/n is n .

So,

$\sqrt[3]{ \sqrt[2]{5} } \\ = \sqrt[6]{5}$

We observe that ,
$\sqrt[3]{ \sqrt[2]{5} }$

is a surd of order 6 .

So ,The correct answer is Option C , 6

:-)

Answer 2

Option ( C ) is correct.

Cube root of √5

= (5½ )^⅓

= 5^( 1/2 × 1/3 )

= 5^1/6

Degree is 6.

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