# Difference between revisions of "2002 AMC 10B Problems/Problem 14"

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== Solution == | == Solution == | ||

− | Taking the squareroot, <math>N=5^{64}\cdot 8^{25}=5^{64}\cdot 2^{75}=10^{64}\cdot 2^{11}</math>. This is <math>2048</math> with | + | Taking the squareroot, <math>N=5^{64}\cdot 8^{25}=5^{64}\cdot 2^{75}=10^{64}\cdot 2^{11}</math>. This is <math>2048</math> with 64 <math>0</math>'s on the end. So, the sum of the digits of <math>N</math> is <math>14\Longrightarrow\mathrm{ (B) \ }</math> |

## Revision as of 13:06, 27 December 2011

## Problem

The number is the square of a positive integer . In decimal representation, the sum of the digits of is

## Solution

Taking the squareroot, . This is with 64 's on the end. So, the sum of the digits of is