https://file.aiquickdraw.com/mathbot/file/17271844699619dyhzk3g.jpg

The expression you have uploaded is:

\[
\left( \sqrt{5} + \sqrt{3} \right)^2
\]

To expand this expression, we'll use the binomial expansion formula:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

Here, \( a = \sqrt{5} \) and \( b = \sqrt{3} \). Now let's expand:

1. \( a^2 = (\sqrt{5})^2 = 5 \)
2. \( b^2 = (\sqrt{3})^2 = 3 \)
3. \( 2ab = 2 \times \sqrt{5} \times \sqrt{3} = 2 \times \sqrt{15} = 2\sqrt{15} \)

Now, putting it all together:

\[
\left( \sqrt{5} + \sqrt{3} \right)^2 = 5 + 3 + 2\sqrt{15} = 8 + 2\sqrt{15}
\]

Thus, the expanded and simplified result is:

\[
8 + 2\sqrt{15}
\]

Would you like further clarification or more details on this?

Here are five related questions to expand your understanding:
1. How would the formula change if the powers were higher, such as \( (\sqrt{5} + \sqrt{3})^3 \)?
2. What if you needed to simplify \( (\sqrt{5} - \sqrt{3})^2 \)?
3. Can you apply this method to an expression like \( (\sqrt{7} + \sqrt{2})^2 \)?
4. What would happen if you combined like terms from two such binomials, such as \( (\sqrt{5} + \sqrt{3})^2 + (\sqrt{5} - \sqrt{3})^2 \)?
5. How do square roots behave under multiplication and division in expressions like these?

**Tip:** When dealing with binomial expansions that involve square roots, focus on simplifying the terms before and after expansion to avoid unnecessary complications!

Kerjakan dengan tepat Dan teliti (√5 + √3)^2

Learn how to expand and simplify the expression (√5 + √3)^2 using the binomial expansion formula. This problem explores key algebraic concepts, including square roots and the binomial theorem. Suitable for students in Grades 9-10.

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