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If $N^2 = (7601)_8$ where $N$ is a positive integer, then the value of $N$ is

1. $(241)_5$
2. $(143)_6$
3. $(165)_7$
4. $(39)_{16}$

edited | 2.1k views
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here 8 is misstyped with g

$N^2 = {(7601)}_8$

$N^2 = 7 * 8^3 + 6 * 8^2 + 0 * 8^1 + 1 * 8^0$

$N^2 = 3969$

$N = 63$

Now consider the option

A. ${(241)}_5 = 2 * 5^2 + 4 * 5^1 + 1 * 5^0 = 50 + 20 + 1 = 71$ (Not an answer)

B. ${(143)}_6 = 1 * 6^2 + 4 * 6^1 + 3 * 6^0 = 36 + 24 + 3 = 63$ (Its the answer)

Rest you can check.

by Boss (35.7k points)
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any short method for this type of Questions....it is tooo time consuming to first convert in decimal then the option .??