# Difference between revisions of "2021 AMC 10B Problems/Problem 2"

## Problem

What is the value of $$\sqrt{(3-2\sqrt{3})^2}+\sqrt{(3+2\sqrt{3})^2}?$$ $\textbf{(A)} ~0 \qquad\textbf{(B)} ~4\sqrt{3}-6 \qquad\textbf{(C)} ~6 \qquad\textbf{(D)} ~4\sqrt{3} \qquad\textbf{(E)} ~4\sqrt{3}+6$

## Solution

Note that the square root of a squared number is the absolute value of the number because the square root function always gives a positive number. We know that $3-2\sqrt{3}$ is actually negative, thus the absolute value is not $3-2\sqrt{3}$ but $2\sqrt{3} - 3$. So the first term equals $2\sqrt{3}-3$ and the second term is $3+2\sqrt3$.

Summed up you get $\boxed{\textbf{(D)} ~4\sqrt{3}}$ ~bjc and abhinavg0627

## Video Solution

https://youtu.be/HHVdPTLQsLc ~Math Python

## Video Solution by OmegaLearn

 2021 AMC 10B (Problems • Answer Key • Resources) Preceded by2021 AMC 10A Followed by2022 AMC 10A 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 10 Problems and Solutions
Invalid username
Login to AoPS