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

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− | + | ==Problem== | |

− | What is the value of <cmath>\sqrt{(3-2\sqrt{ | + | What is the value of <cmath>\sqrt{(3-2\sqrt{3})^2}+\sqrt{(3+2\sqrt{3})^2}?</cmath> |

<math>\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</math> | <math>\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</math> | ||

− | + | ==Solution== | |

− | + | Note that the square root of a squared number is the absolute value of the number. | |

− | + | So the first term equals <math>2\sqrt{3}-3</math> and the second term is <math>3+2\sqrt3</math> | |

+ | Summed up you get <math>\boxed{\textbf{(D)} ~4\sqrt{3}}</math>~bjc |

## Revision as of 18:29, 11 February 2021

## Problem

What is the value of

## Solution

Note that the square root of a squared number is the absolute value of the number. So the first term equals and the second term is Summed up you get ~bjc