Math, asked by tiwarinilesh2019, 6 months ago

What is the order of the surd ∜(√5)​

Answers

Answered by pulakmath007
2

SOLUTION

TO DETERMINE

The order of the surd

 \displaystyle \sf{  \sqrt[4]{( \sqrt{5} )}  }

CONCEPT TO BE IMPLEMENTED

Order of a Surd :

If an irrational numbers can be written in the form  \sf{ \sqrt[n]{x} }

Where x is a rational number and n is a natural number

 \sf{Then \: \: n \: \: is \: the \: order \: of \: the \: surd \: \: \sqrt[n]{x} }

EVALUATION

Here the given surd is

 \displaystyle \sf{  \sqrt[4]{( \sqrt{5} )}  }

This can simplified as below

 \displaystyle \sf{  \sqrt[4]{( \sqrt{5} )}  }

 \displaystyle \sf{  =   { \bigg(  \sqrt{5} \bigg)}^{ \frac{1}{4} }  }

 \displaystyle \sf{  =   { \bigg(  {5}^{ \frac{1}{2} }  \bigg)}^{ \frac{1}{4} }  }

 \displaystyle \sf{  =   { \bigg(  5 \bigg)}^{  \frac{1}{2}  \times \frac{1}{4} }  }

 \displaystyle \sf{  =   { \bigg(  5 \bigg)}^{  \frac{1}{8}  }  }

 \displaystyle \sf{  = \sqrt[8]{5}   }

Comparing with  \sf{ \sqrt[n]{x} }

n = 8 , x = 5

Hence the order of the surd = 8

FINAL ANSWER

The order of the surd = 8

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