Question

find square root of : 18i​

Answer 1

Square root of 18i is $\pm 3(1+i)$

Step-by-step explanation:

To find : Square root of $18i$

Solution :

The factor of 18 is

$18=2\times 3\times 3$

Taking root,

$\sqrt{18}=\sqrt{2\times 3\times 3}$

$\sqrt{18}=3\sqrt{2}$

The square root of i is

$\sqrt{i}=\pm\frac{1}{\sqrt{2}}(1+i)$

So, $\sqrt{18i}=\sqrt{18}\times \sqrt{i}$

$\sqrt{18i}=3\sqrt{2}\times \pm\frac{1}{\sqrt{2}}(1+i)$

$\sqrt{18i}=\pm 3(1+i)$

Therefore, square root of 18i is $\pm 3(1+i)$

#Learn more

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