The expression you provided is:

\[
\sqrt{27} + \sqrt{75}
\]

To simplify, we first break down the square roots:

\[
\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}
\]
\[
\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}
\]

Now we add them together:

\[
\sqrt{27} + \sqrt{75} = 3\sqrt{3} + 5\sqrt{3} = (3 + 5)\sqrt{3} = 8\sqrt{3}
\]

Thus, the simplified form is:

\[
8\sqrt{3}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify square roots of non-perfect squares?
2. What are the rules for adding radical expressions?
3. How can you factor out a common square root from an expression?
4. What is the value of \(\sqrt{3}\) in decimal form?
5. How do you simplify a difference involving square roots?

**Tip:** When simplifying square roots, always look for perfect squares that you can factor out.

Learn how to simplify the expression √27 + √75 by breaking down the square roots and combining like terms. This solution demonstrates the addition of radicals, perfect square factorization, and simplification techniques. Ideal for students in Grades 7-10.

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