https://file.aiquickdraw.com/mathbot/file/17274445160509tgnjz7t.jpg

The equation provided is:

\[
\sqrt{14 - 8\sqrt{3}} = \sqrt{a} - \sqrt{b}
\]

From solving, we find that:

\[
a = \left( \sqrt{b} + \sqrt{2} \cdot \sqrt{7 - 4\sqrt{3}} \right)^2
\]

Now, simplifying the expression will allow us to find \(a - b\). I'll proceed with the simplification.The expression for \( a - b \) is:

\[
a - b = \left( \sqrt{b} + \sqrt{2} \cdot \sqrt{7 - 4\sqrt{3}} \right)^2 - b
\]

We can further evaluate this to find the numerical value of \( a - b \). Let me complete this calculation.The expression for \( a - b \) simplifies to:

\[
a - b = -\sqrt{3} + \left( \sqrt{2} \cdot \sqrt{7 - 4\sqrt{3}} + \sqrt[4]{3} \right)^2
\]

Now, let me approximate the numerical value to determine the correct choice.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you would like to manually simplify or compute the result, we were attempting to evaluate the expression numerically:

\[
a - b = -\sqrt{3} + \left( \sqrt{2} \cdot \sqrt{7 - 4\sqrt{3}} + \sqrt[4]{3} \right)^2
\]

Would you like me to proceed differently or clarify anything else?

Here are five related questions for further exploration:

1. How can we solve radical equations with nested square roots?
2. What is the relationship between the numbers in radical simplification problems?
3. How can approximations help simplify complex root expressions?
4. What methods can be used to compare values in radical expressions?
5. How do we simplify expressions involving mixed radicals like \(\sqrt{2} \cdot \sqrt{7 - 4\sqrt{3}}\)?

**Tip**: When simplifying radicals, always check for common patterns or identities that might simplify your work.

Perhatikan persamaan berikut: √(14 - 8√3) = √a - √b. Dengan a > b, maka nilai a - b adalah ...

Learn how to solve the equation √(14 - 8√3) = √a - √b with detailed step-by-step simplification, exploring algebraic concepts of radicals. Find the correct value of a - b. Suitable for Grades 10-12.

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