Question

The order of the surd 2187 after simplification is​

Answer 1

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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