If three positive real numbers a,b,c are in A.P. such that abc=4 then the minimum possible value of b is

If three positive real numbers $a, b, c$ are in A.P. such that $a b c = 4$ then the minimum possible value of b is

$a, b, c$ are in A.P

$\Rightarrow 2 b = a + c$

$a b c = 4$

$A . M \geq G . M$

$\frac{a + b + c}{3} \geq \sqrt[3]{a b c}$

$\frac{2 b + b}{3} \geq \sqrt[3]{4}$

$b \geq \sqrt[3]{4}$

$b \geq 2^{\frac{2}{3}}$

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