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oops. Fixed less to more
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Christi committed Jul 2, 2012
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<p><code><var>N * N</var></code> is the nearest perfect square less than <code><var>Q</var></code>.</p>
<p><code><var>(N + 1) * (N + 1)</var></code> is the nearest perfect square less than <code><var>Q</var></code>.</p>
<p><code><var>(N + 1) * (N + 1)</var></code> is the nearest perfect square more than <code><var>Q</var></code>.</p>
<p>So, we know <code><var>N * N</var> &lt; <var>Q</var> &lt; <var>(N + 1) * (N + 1)</var></code>.</p>
<p>So, <code>\sqrt{<var>N * N</var>} &lt; \sqrt{<var>Q</var>} &lt; \sqrt{<var>(N + 1)*(N + 1)</var>}</code>.</p>
<p class="final_answer">So the square root of <code><var>Q</var></code> is between <code><var>N</var></code> and <code><var>N + 1</var></code>.</p>
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