Finding Square Root of a Square Root

Number Theory Level 3

If $x$ and $y$ are integers, each greater than one, and they satisfy the relationship, $y= \sqrt{x \sqrt{x \sqrt{x \sqrt x}}}$ , determine the smallest value of $x+y$ .

98304 48567 12345 93846 94673

1 solution

Kay Xspre
Jan 14, 2016

We can wrote this question as $y = x^{\frac{15}{16}}$ . Here, when $1 < x$ , the smallest $x$ such that $y$ is integer is $x = 2^{16} = 65536$ , and $y=2^{15} = 32768$ . Hence, $x+y = 98304$

thanks for the solution ^_^

king james Palma - 5 years, 5 months ago

Finding Square Root of a Square Root

1 solution

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