https://file.aiquickdraw.com/mathbot/file/1730343070375rdnpdh3h.jpg

solve it the easiest n fastest way  
Plsss solve it in easy way so I can understand im slow at math 

Let's solve these square root problems step-by-step.

---

### Problem #10
\[
\sqrt{9x^2 y^5}
\]

1. **Separate into Square Roots**: Break down each term:
   \[
   \sqrt{9} \times \sqrt{x^2} \times \sqrt{y^5}
   \]

2. **Simplify Each Term**:
   - \(\sqrt{9} = 3\)
   - \(\sqrt{x^2} = x\) (since \(x^2\) is a perfect square)
   - For \(\sqrt{y^5}\), separate \(y^5\) as \(y^4 \times y\):
     \[
     \sqrt{y^5} = \sqrt{y^4 \times y} = \sqrt{y^4} \times \sqrt{y} = y^2 \sqrt{y}
     \]

3. **Combine the Terms**:
   \[
   \sqrt{9x^2 y^5} = 3 \cdot x \cdot y^2 \cdot \sqrt{y} = 3xy^2 \sqrt{y}
   \]

So, the answer for #10 is:
\[
3xy^2 \sqrt{y}
\]

---

### Problem #12
\[
\sqrt{32a^4b^7}
\]

1. **Separate into Square Roots**:
   \[
   \sqrt{32} \times \sqrt{a^4} \times \sqrt{b^7}
   \]

2. **Simplify Each Term**:
   - \(\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}\)
   - \(\sqrt{a^4} = a^2\) (since \(a^4\) is a perfect square)
   - For \(\sqrt{b^7}\), separate \(b^7\) as \(b^6 \times b\):
     \[
     \sqrt{b^7} = \sqrt{b^6 \times b} = \sqrt{b^6} \times \sqrt{b} = b^3 \sqrt{b}
     \]

3. **Combine the Terms**:
   \[
   \sqrt{32a^4b^7} = 4 \cdot a^2 \cdot b^3 \cdot \sqrt{2} \cdot \sqrt{b} = 4a^2b^3 \sqrt{2b}
   \]

So, the answer for #12 is:
\[
4a^2b^3 \sqrt{2b}
\]

---

Would you like more details on any part of the solution, or do you have any specific questions?

### Related Questions to Explore
1. How do you simplify square roots with variables?
2. What is the difference between perfect squares and non-perfect squares?
3. How do you handle square roots when there are fractional exponents?
4. How can you identify terms that can be simplified inside a square root?
5. Why is it helpful to break down terms into their factors?

### Tip:
When simplifying square roots with variables, separate each component (constants and variables) and look for any perfect squares. This makes it easier to simplify each part individually.

Solve #10 and #12 involving square roots with whole numbers and variables.

Learn to simplify square roots that involve whole numbers and variables with exponents. Problems #10 and #12 include step-by-step solutions using square root properties, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation