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Find the value of \(\sqrt{30-\sqrt{30-\sqrt{30-\sqrt{30-\sqrt{.....}}}}}\space?\space \) 
1. 5
2. \(\sqrt{30}\space\)
3. 5.4
4. 6

1 Answer

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Correct Answer - Option 1 : 5

Given:

\(√{30-√{30-√{30-√{30-√{.....}}}}}\space?\space \)

Calculation:

Let x be the value of \(√{30-√{30-√{30-√{30-√{.....}}}}}\space?\space \)

Then,

⇒ x = √30 – x

squaring both sides we get,

⇒ x2 = 30 – x

⇒ x2 + x + 30 = 0

⇒ x2 + 6x – 5x + 30 = 0

⇒ x(x + 6) – 5(x + 6) = 0

⇒ (x – 5) (x + 6) = 0

⇒ x = 5 or -6

∴ The required value is 5

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