Find the value of \(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + .

1.	Find the value of \(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...\,\,...\,\,...\,\,...\,\,...\,\,.\,\infty } } } } \)1. 32. 53. 64. 4
Answer» Correct Answer - Option 3 : 6 Given: \(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...\,\,...\,\,...\,\,...\,\,...\,\,.\,\infty } } } } \) Calculation: Let 'a' be the value of \(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...\,\,...\,\,...\,\,...\,\,...\,\,.\,\infty } } } } \) ⇒ a = \(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...\,\,...\,\,...\,\,...\,\,...\,\,.\,\infty } } } } \) Squaring both sides, we get ⇒ a² = 30 + \(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...\,\,...\,\,...\,\,...\,\,...\,\,.\,\infty } } } } \) ⇒ a² = 30 + a ⇒ a² - a - 30 = 0 ⇒ a² - 6a + 5a - 30 = 0 ⇒ (a - 6)(a + 5) = 0 ⇒ a = 6, -5 a = - 5 is not possible ∴ The value of \(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...\,\,...\,\,...\,\,...\,\,...\,\,.\,\infty } } } } \) is 6.

Find the value of \(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...\,\,...\,\,...\,\,...\,\,...\,\,.\,\infty } } } } \)1. 32. 53. 64. 4

Answer» Correct Answer - Option 3 : 6

Given:

\(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...\,\,...\,\,...\,\,...\,\,...\,\,.\,\infty } } } } \)

Calculation:

Let 'a' be the value of \(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...\,\,...\,\,...\,\,...\,\,...\,\,.\,\infty } } } } \)

⇒ a = \(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...\,\,...\,\,...\,\,...\,\,...\,\,.\,\infty } } } } \)

Squaring both sides, we get

⇒ a² = 30 + \(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...\,\,...\,\,...\,\,...\,\,...\,\,.\,\infty } } } } \)

⇒ a² = 30 + a

⇒ a² - a - 30 = 0

⇒ a² - 6a + 5a - 30 = 0

⇒ (a - 6)(a + 5) = 0

⇒ a = 6, -5

a = - 5 is not possible

∴ The value of \(\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...\,\,...\,\,...\,\,...\,\,...\,\,.\,\infty } } } } \) is 6.