Nested Radical

Algebra Level 2

125 5 sqrt(5) 25

Nabil Moustafa by Nabil Moustafa , 37, Egypt

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2 solutions

Md Omur Faruque
Oct 5, 2015

Let,

x = 25 25 25 … 3 3 3 x=\sqrt[3]{25\sqrt[3]{25\sqrt[3]{25\dots}}} ⇒ x 3 = 25 × 25 25 25 … 3 3 3 \Rightarrow x^3=25\times \sqrt[3]{25\sqrt[3]{25\sqrt[3]{25\dots}}} ⇒ x 3 = 25 × x \Rightarrow x^3=25\times x ⇒ x 2 = 25 [ As, x ≠ 0 ] \Rightarrow x^2=25\,\color{#0C6AC7} {[\text{As, } x\neq0]} ⇒ x = 5 [ As, x > 0 ] \Rightarrow x= \color{#69047E} {\boxed 5}\, \color{#0C6AC7} {[\text{As, } x>0]}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Nabil Moustafa
Oct 5, 2015

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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