https://file.aiquickdraw.com/mathbot/file/1730082972035ubs0po6y.jpg

To simplify the expression:

\[
\sqrt{64x^{12}y^{26}}
\]

we'll follow these steps:

### Step 1: Simplify the Square Root of Each Factor
Since we have a square root, we can take the square root of each term separately.

1. **Square root of 64**: 
   \[
   \sqrt{64} = 8
   \]

2. **Square root of \( x^{12} \)**:
   \[
   \sqrt{x^{12}} = x^{\frac{12}{2}} = x^6
   \]

3. **Square root of \( y^{26} \)**:
   \[
   \sqrt{y^{26}} = y^{\frac{26}{2}} = y^{13}
   \]

### Step 2: Combine the Results
Now, putting it all together:

\[
\sqrt{64x^{12}y^{26}} = 8x^6y^{13}
\]

### Final Answer
\[
8x^6y^{13}
\]

Would you like further details or have any questions?

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Here are some related questions that might help you expand on this concept:

1. How would the solution change if the exponent on \( y \) was an odd number?
2. What if we had a cube root instead of a square root in this problem?
3. Can we apply the same method to simplify \(\sqrt{81x^{10}y^{20}}\)?
4. How do we handle variables with negative exponents under a square root?
5. What is the general formula for simplifying \(\sqrt{a^m b^n}\) when \( m \) and \( n \) are even numbers?

**Tip:** When simplifying square roots with variables, remember to divide exponents by 2 if they’re even for a straightforward result.

Simplify the expression \( \sqrt{64x^{12}y^{26}} \). Assume that all expressions under radicals represent nonnegative numbers.

Learn how to simplify the square root of the expression 64x^12y^26 with a detailed step-by-step solution. This problem covers key algebraic concepts including radicals and exponents. Suitable for students in Grades 8-10.

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