Express in simplest radical form. \[ \sqrt{25 x^{13}} \] Answer \( \sqrt{25 x^{13}} \) \( x^{6} \sqrt{25 x} \) \( 5 x^{6} \sqrt{x} \) \( 5 \sqrt{x^{13}} \)

To simplify \( \sqrt{25 x^{13}} \), we recognize that the square root can be distributed over the multiplication of terms. First, we note that \( \sqrt{25} = 5 \) because 5 is the number that, when multiplied by itself, equals 25. Now, for \( x^{13} \), we apply the property of square roots which tells us \( \sqrt{x^{2n}} = x^n \). We can split \( x^{13} \) as \( x^{12} \cdot x \), where \( 12 \) is an even exponent. Therefore, \( \sqrt{x^{12}} = x^6 \). Putting it all together, we have: \[ \sqrt{25 x^{13}} = \sqrt{25} \cdot \sqrt{x^{12} \cdot x} = 5 \cdot x^6 \cdot \sqrt{x} = 5 x^6 \sqrt{x}. \] So, the simplest radical form is: \[ 5 x^{6} \sqrt{x}. \]