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The expression you provided is:

\[
\sqrt{5} + \sqrt{27} - \sqrt{125} + \sqrt{75}
\]

Let's simplify each square root:

1. \(\sqrt{5}\) remains as \(\sqrt{5}\).
2. \(\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}\).
3. \(\sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}\).
4. \(\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}\).

Now, substitute these back into the expression:

\[
\sqrt{5} + 3\sqrt{3} - 5\sqrt{5} + 5\sqrt{3}
\]

Next, combine like terms:

- \(\sqrt{5} - 5\sqrt{5} = -4\sqrt{5}\)
- \(3\sqrt{3} + 5\sqrt{3} = 8\sqrt{3}\)

Thus, the simplified expression is:

\[
-4\sqrt{5} + 8\sqrt{3}
\]

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. How do you simplify more complex square roots?
2. What is the process for combining like terms in radical expressions?
3. How do you handle expressions with cube roots or higher?
4. What is the difference between rational and irrational numbers?
5. How can square roots be expressed in decimal form?

**Tip:** Always break down the square roots into their prime factors to simplify them properly.

Hitung hasil dari √5 + √27 - √125 + √75

Learn how to simplify the expression √5 + √27 - √125 + √75. This problem demonstrates how to break down square roots into prime factors and combine like terms. Suitable for students in Grades 8-10.

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