An algebra problem by kritarth lohomi

Algebra Level 1

x = 2 \sqrt{\sqrt{\sqrt{x}}} = 2

Solve for x


The answer is 256.

Kritarth Lohomi by kritarth lohomi , 18, India

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3 solutions

x = 2 ( ( x 1 2 ) 1 2 ) 1 2 = 2 x 1 8 = 2 ( x 1 8 ) 8 = 2 8 x = 256 \sqrt{\sqrt{\sqrt{x}}}=2\\ ((x^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}}=2\\ x^{\frac{1}{8}}=2\\ (x^{\frac{1}{8}})^8=2^8 \\ \boxed{x=256}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

X^1/8=(256)^1/8 since 2^8=256

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Adrian Cadiz
Feb 7, 2015

sqrt(sqrt(sqrt(x)))=2 sqrt(sqrt(x))=2^2 sqrt(x)=2^4 x=2^8 x=256

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