Question

root 3power n =27 then 5 n root 64​

Answer 1

SOLUTION

GIVEN

$\sf{ {( \sqrt{3} )}^{n} = 27}$

TO DETERMINE

$\sf{ \sqrt[n]{64} }$

EVALUATION

Here it is given that

$\sf{ {( \sqrt{3} )}^{n} = 27}$

Now we find the value of n

$\sf{ {( \sqrt{3} )}^{n} = 27}$

$\sf{ \implies \: {( \sqrt{3} )}^{n} = {(3)}^{3} }$

$\sf{ \implies \: {( \sqrt{3} )}^{n} = {( \sqrt{3} )}^{6} }$

$\sf{ \implies \: n = 6}$

Now

$\sf{ \sqrt[n]{64} }$

$\sf{ = \sqrt[6]{64} }$

$= 2$

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