$\sqrt[4]{-49}$এর মান কোনটি ? 

$\begin{aligned} & \text { ধরি, } \\ \Rightarrow & =\sqrt[4]{-49} \\ \Rightarrow & x^{4}=-49 \\ \Rightarrow & \left(x^{2}\right)^{2}=(7 i)^{2} \\ \Rightarrow & x^{2}= \pm \sqrt{(7 i)^{2}} \\ \Rightarrow & x^{2}= \pm 7 i \\ \Rightarrow & x^{2}=\frac{7}{2} \cdot \pm 2 i \\ \Rightarrow & x^{2}=\frac{7}{2}(1 \pm 2 i-1) \\ \Rightarrow & x^{2}=\frac{7}{2}\left(1^{2} \pm 2 \cdot 1 \cdot i+l^{2})\right. \\ \Rightarrow & x^{2}=\frac{7}{2} \cdot(1 \pm i)^{2} \\ \Rightarrow & x= \pm \sqrt{7 / 2}(1 \pm i) \\ \therefore & \sqrt{-49}= \pm \sqrt{\frac{7}{2}}(1 \pm i) \end{aligned}$

শর্টকাট:

$\begin{array}{l}\sqrt[4]{-n^{2}}= \pm \sqrt{\frac{n}{2}}(1 \pm i) \\ \therefore \sqrt[4]{-49} \\ =\sqrt[4]{-{7}^{2}} \text { এখানে } \\ n=7 \\ \therefore \sqrt[4]{-49}= \pm \sqrt{\frac{7}{2}}(1 \pm i) \\\end{array}$