https://file.aiquickdraw.com/mathbot/file/1725981763018cb5330h3.png

The given expression is:

\[
\sqrt{3} - 4\sqrt{27} = 2\sqrt{\boxed{\phantom{2}}}
\]

Let's simplify it step by step:

1. First, simplify \( 4\sqrt{27} \).
   - \( \sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3} \)
   - Therefore, \( 4\sqrt{27} = 4 \times 3\sqrt{3} = 12\sqrt{3} \)

2. Now the equation becomes:
   \[
   \sqrt{3} - 12\sqrt{3} = 2\sqrt{\boxed{\phantom{2}}}
   \]

   Combine like terms on the left-hand side:
   \[
   (1 - 12)\sqrt{3} = -11\sqrt{3}
   \]

   So we have:
   \[
   -11\sqrt{3} = 2\sqrt{\boxed{\phantom{2}}}
   \]

3. To solve for the boxed term, divide both sides by 2:
   \[
   \sqrt{\boxed{\phantom{2}}} = \frac{-11\sqrt{3}}{2}
   \]

   Squaring both sides to remove the square root:
   \[
   \boxed{\phantom{2}} = 3
   \]

Thus, the complete equation is:

\[
\sqrt{3} - 4\sqrt{27} = 2\sqrt{3}
\]

Would you like further clarification or details on any part? Here are 5 follow-up questions related to this topic:

1. How do you simplify radicals like \( \sqrt{27} \)?
2. What are some techniques to handle addition or subtraction of like radicals?
3. Can you provide an example involving multiplication of radicals?
4. What would change in the process if you had an equation with cube roots instead of square roots?
5. How do we rationalize the denominator of a fraction involving radicals?

**Tip:** Always look for common factors inside the radicals to simplify them first.

Complete the expression subtracting the radicals: \(\sqrt{3} - 4\sqrt{27} = 2\sqrt{\boxed{\phantom{2}}}\).

Learn how to simplify and subtract radicals in the expression \(\sqrt{3} - 4\sqrt{27}\). This problem involves radical simplification and subtraction techniques, suitable for Grades 8-10. Includes step-by-step guidance.

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