Find the value of \sqrt {2\sqrt {{2}{ {{\sqrt2}}\sqrt{{ 2} {{\sqrt2 }\sqrt2}}}}}.... .

SSC CPO SI and ASI Model Paper 2

Question : 130 of 200

Marks: +1, -0

Find the value of $√ {2√ {{2}{ {{√2}}√{{ 2} {{√2 }√2}}}}}.... .$

Solution:

(4) Let

√ {√2 √2 √2 √2 √2 √2}

.... = x
After squaring both sides, we get

2√ {√2√ 2√ 2 √2 √2 √2}..... = x^2

⇒ x^2 = 2x

⇒x2 – 2x = 0

⇒ x = 2 or 0 (x ≠ 0 as value of √2is greater than 1)

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