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

$\sqrt{1} + \sqrt{1+3} + \sqrt{1+3+5} + \sqrt{1+3+5+7}$ = $\sqrt{1} + \sqrt{4} + \sqrt{9} + \sqrt{16}\ = 1 + 2 + 3 + 4 = \boxed{\textbf{(C) 10}}$

Note: This comes from the fact that the sum of the first $n$ odds is $n^2$ .

Video Solution

https://youtu.be/WfTty8Fe5Fo

~IceMatrix

2020 AMC 12B (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

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2020 AMC 12B Problems/Problem 1

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Video Solution

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