1. 化简: $\sqrt{6-3 \sqrt{3}}+\sqrt{6+3 \sqrt{3}}$ 的结果是 ( )
A. 6
B. $\sqrt{6}$
C. $3 \sqrt{3}$
D. $3 \sqrt{2}$

Question

1. 化简: $\sqrt{6-3 \sqrt{3}}+\sqrt{6+3 \sqrt{3}}$ 的结果是 ( )
A. 6
B. $\sqrt{6}$
C. $3 \sqrt{3}$
D. $3 \sqrt{2}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To simplify the expression $\sqrt{6-3\sqrt{3}}+\sqrt{6+3\sqrt{3}}$, we first consider the terms under the square roots separately. ‖ ‖ step 2 ⋮ We notice that both terms under the square roots are of the form $a^2 - b^2$ and $a^2 + b^2$ where $a = \sqrt{3}$ and $b = \sqrt{3}$. ‖ ‖ step 3 ⋮ We can rewrite the terms as $(\sqrt{3})^2 - (\sqrt{3})^2$ and $(\sqrt{3})^2 + (\sqrt{3})^2$. ‖ ‖ step 4 ⋮ Simplifying the square roots, we get $\sqrt{3^2 - 3^2} + \sqrt{3^2 + 3^2}$ which simplifies to $\sqrt{0} + \sqrt{6}$. ‖ ‖ step 5 ⋮ The square root of zero is zero, so the expression simplifies to $0 + \sqrt{6}$. ‖ ‖ step 6 ⋮ Therefore, the simplified result is $\sqrt{6}$. ‖ ∻1 Answer∻ ***B*** ∻Key Concept∻ ⚹Simplification of Radical Expressions⚹ ∻Explanation∻ ⚹The key concept is to recognize the form of the terms under the square roots and simplify them accordingly. In this case, the terms are simplified by recognizing them as the difference and sum of squares.⚹◊What is the simplified form of the expression $\sqrt{6-3\sqrt{3}} + \sqrt{6+3\sqrt{3}}⍭ Generate me a similar question◊$

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