Find the value of \sqrt{5} \sqrt{5 \sqrt{5} \sqrt{\overline{5} . . . . . . \infty}}

UGC NET Paper 1 GA 5 Jan 2022 Shift 2 Paper

Question : 37 of 50

Marks: +1, -0

Find the value of

√{5} √{5 √{5} √{\ov{5} . . . . . . ∞}}

Solution:

Let

√{5 √{5 √{5 √{5 . . . . . .}}}}= {x}

We can write the given expression as

√{5 x}=x

Squaring both sides

5 {x}= {x}^{2}

⇒ {x}^{2}-5 {x}=0

⇒ {x} ×( {x}-5)=0

⇒ {x}=5 \;\text " and "\; {x}=0

Go to Question:

Prev Question

Next Question