Question

If s(a) denotes square root of a,find s(12+s(12+s(12...Upto infinity

Answer 1

Question :

$\sqrt{12 + \sqrt{12 \: + \sqrt{12} + \sqrt{12}}}....$

Assume that ,

$\sqrt{12 + \sqrt{12 \: + \sqrt{12} + \sqrt{12}}} \: = m \: + 1$

Where, 12 = m (m+1)

12 = m (m+1) Now, LCM of 12 = 4 × 3

12 = m (m+1) Now, LCM of 12 = 4 × 3 Substitute the Value of m = 4 , i.e m ( m+1)

12 = m (m+1) Now, LCM of 12 = 4 × 3 Substitute the Value of m = 4 , i.e m ( m+1) 3 ( 3+1)

12 = m (m+1) Now, LCM of 12 = 4 × 3 Substitute the Value of m = 4 , i.e m ( m+1) 3 ( 3+1) = 3 ( 4 )

12 = m (m+1) Now, LCM of 12 = 4 × 3 Substitute the Value of m = 4 , i.e m ( m+1) 3 ( 3+1) = 3 ( 4 ) = 12

12 = m (m+1) Now, LCM of 12 = 4 × 3 Substitute the Value of m = 4 , i.e m ( m+1) 3 ( 3+1) = 3 ( 4 ) = 12 Therefore, Required Value of

$\sqrt{12 + \sqrt{12 \: + \sqrt{12} + \sqrt{12}}} = \sf{3 \: + 1} \\ \\ \sqrt{12 + \sqrt{12 \: + \sqrt{12} + \sqrt{12}}} = \sf{4}$