Question

the order of the surd 6√729 after simplified is see attachment or photo​

Answer 1

Answer:

d) Not a surd

Step-by-step explanation:

if you multiple 3

6 times then you will get 729

Surd means there should be not any number that can be simplified by the root

but here 3√729 exists

Therefore, it's not a surd

Answer 2

${\underline{\underline{\red{\bf{What\:is\:surd?:}}}}}$

• A root of a positive real quantity is called a surd if its value can't be exactly determined.

$\underline{\purple{\bf{Order\:of\:surd:}}}$

• Let us consider a surd ⁿ√m , here n is called the order of the surd.

Now , given surd is ⁶√729.

Lets simply this ,

729 can be written as 27 × 27 = 3³ × 3³ = 3⁶.

This becomes , ⁶√3⁶ = $\sf{3^{\frac{1}{6}\times6}}$ = 3¹ = 3 = 3/1.

Hence after simplification the number is not a surd , but it is a rational number , since it can be expressed in the form of p/q where p and q are integers and q ≠0.

Hence the correct option is (a) .

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Some more information:

${\underline{\underline{\red{\bf{\dag Rational\: Number:}}}}}$

• The numbers in the form of p/q where p and q are integers and q ≠ 0 , are called Rational numbers.
• Ex - 2 , ¾ -7 ,9 , etc.

${\underline{\underline{\red{\bf{\dag Integers :}}}}}$

• All counting numbers their negatives along with 0 are called integers.
• Ex - 0,-1,-3,6, etc.