2020 AMC 12B Problems/Problem 1

Problem

What is the value in simplest form of the following expression? $\sqrt{1} + \sqrt{1+3} + \sqrt{1+3+5} + \sqrt{1+3+5+7}$ $\textbf{(A) }5 \qquad \textbf{(B) }4 + \sqrt{7} + \sqrt{10} \qquad \textbf{(C) } 10 \qquad \textbf{(D) } 15 \qquad \textbf{(E) } 4 + 3\sqrt{3} + 2\sqrt{5} + \sqrt{7}$

Solution

$\sqrt{1} + \sqrt{1+3} + \sqrt{1+3+5} + \sqrt{1+3+5+7}$ = $1 + 2 + 3 + 4$ = $\boxed{\textbf{(C) 10}}$

2020 AMC 12B (Problems • Answer Key • Resources)
Preceded by First Problem	Followed by Problem 2
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All AMC 12 Problems and Solutions

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2020 AMC 12B Problems/Problem 1

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