https://r2.erweima.ai/mathbot/image/1725710331548sd9d1waa.jpg

Let's simplify the square roots from the exercises shown in the image:

### Ejercicio 1: Simplifica la expresión \(\sqrt{50}\)

To simplify \(\sqrt{50}\), we find the prime factorization of 50:

\[
50 = 2 \times 5^2
\]

Now, we can rewrite the square root as:

\[
\sqrt{50} = \sqrt{2 \times 5^2}
\]

Since \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), this becomes:

\[
\sqrt{50} = \sqrt{2} \times \sqrt{5^2} = \sqrt{2} \times 5 = 5\sqrt{2}
\]

So, the simplified form is:

\[
\sqrt{50} = 5\sqrt{2}
\]

### Ejercicio 2: Simplifica la expresión \(\sqrt{72}\)

To simplify \(\sqrt{72}\), we find the prime factorization of 72:

\[
72 = 2^3 \times 3^2
\]

Now, we can rewrite the square root as:

\[
\sqrt{72} = \sqrt{2^3 \times 3^2}
\]

Applying the square root to each factor:

\[
\sqrt{72} = \sqrt{2^3} \times \sqrt{3^2} = \sqrt{2^2 \times 2} \times \sqrt{3^2}
\]

Simplify further:

\[
\sqrt{72} = 2\sqrt{2} \times 3 = 6\sqrt{2}
\]

So, the simplified form is:

\[
\sqrt{72} = 6\sqrt{2}
\]

### Summary of Simplified Results:

1. \(\sqrt{50} = 5\sqrt{2}\)
2. \(\sqrt{72} = 6\sqrt{2}\)

Would you like more details on these steps, or do you have any specific questions?

Here are five related questions you may find useful:

1. How do you simplify square roots of other numbers, like \(\sqrt{75}\)?
2. What are the properties of square roots that help in simplifying them?
3. How can you apply these methods to simplify expressions involving cube roots?
4. How do you rationalize the denominator in expressions with square roots?
5. How do you add or subtract expressions involving square roots?

**Tip:** Always look for perfect squares in the factorization to simplify square roots easily!

Simplify the following expressions: 
1. \(\sqrt{50}\) 
2. \(\sqrt{72}\)

Learn how to simplify the square roots of 50 and 72 using prime factorization and square root properties. This problem covers essential algebraic concepts for Grades 8-10 students.

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