MathDB
Differences between squares

Source: 2020 AMC 12B #1

February 6, 2020
AMCAMC 12AMC 12 B2020 AMC 12B2020 AMC

Problem Statement

What is the value in simplest form of the following expression? 1+1+3+1+3+5+1+3+5+7\sqrt{1} + \sqrt{1+3} + \sqrt{1+3+5} + \sqrt{1+3+5+7}
<spanclass=′latex−bold′>(A)</span>5<spanclass=′latex−bold′>(B)</span>4+7+10<spanclass=′latex−bold′>(C)</span>10<spanclass=′latex−bold′>(D)</span>15<spanclass=′latex−bold′>(E)</span>4+33+25+7<span class='latex-bold'>(A) </span>5 \qquad <span class='latex-bold'>(B) </span>4 + \sqrt{7} + \sqrt{10} \qquad <span class='latex-bold'>(C) </span> 10 \qquad <span class='latex-bold'>(D) </span> 15 \qquad <span class='latex-bold'>(E) </span> 4 + 3\sqrt{3} + 2\sqrt{5} + \sqrt{7}
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