Math, asked by tanishakitawat, 3 months ago

The order of the surd 2187 after simplification is​

Answers

Answered by pulakmath007
3

SOLUTION

TO DETERMINE

The order of the surd after simplification

 \sf{ \sqrt[6]{2187} }

EVALUATION

Here the given surd is

 \sf{ \sqrt[6]{2187} }

Now

 \sf{ 2187 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3}

 \sf{  \implies \: 2187 = {3}^{7} }

 \sf{  \implies \: 2187 = {3}^{6} \times 3 }

Thus we get

 \sf{    \sqrt[6]{2187}  = \sqrt[6]{ {3}^{6}  \times 3}  }

 \sf{  \implies  \sqrt[6]{2187}  =3 \:  \sqrt[6]{  3}  }

This states that the order of the surd is 6

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