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√(7-30√-2)

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Let, (a + ib)2 = 7 - 30√2 i

Now using, (a + b)2 = a2 + b2 + 2ab

⇒ a2 + (bi)2 + 2abi = 7 - 30√2 i

Since i2 = -1

⇒ a2 - b2 + 2abi = 7 - 30√2 i

Now, separating real and complex parts, we get

⇒ a2 - b2 = 7 …………..eq.1

⇒ 2ab = 30√2 …….. eq.2

⇒ a = \(\frac{15\sqrt2}{b}\)

Now, using the value of a in eq.1, we get

⇒ \((\frac{15\sqrt2}{b})^2\) – b2 = 7

⇒ 450 – b4 = 7b2

⇒ b4+ 7b2 - 450 = 0

Simplify and get the value of b2, we get,

⇒ b2 = -25 or b2 = 18

As b is real no. so, b2 = 18

b = 3√2 or b = -3√2

Therefore, a = 5 or a = - 5

Hence the square root of the complex no. is 5 + 3√2 i and - 5 - 3√2 i.

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