How to solve this equation [tex]\sqrt{x} 12\\[/tex]34
[tex]\sqrt[n]{x} 56 \\757[/tex]

It looks like there's some confusion with the formatting of the equation. I'll try to interpret it based on what you might have meant. It seems like you are asking how to solve an equation involving square roots and potentially other roots. Here’s a general approach to solving equations involving roots:### Example Equation:\[ \sqrt{x} = 12 \]\[ \sqrt[n]{x} = 56 \]Let's solve these step-by-step:1. **Solve \( \sqrt{x} = 12 \)**   To isolate \( x \), square both sides of the equation:   \[   (\sqrt{x})^2 = 12^2   \]   Simplify:   \[   x = 144   \]2. **Solve \( \sqrt[n]{x} = 56 \)**   Here, \( \sqrt[n]{x} \) is the \( n \)-th root of \( x \). To find \( x \), raise both sides to the power of \( n \):   \[   (\sqrt[n]{x})^n = 56^n   \]   Simplify:   \[   x = 56^n   \]### Combine Solutions:Since you already found \( x = 144 \) from the first equation, substitute \( x = 144 \) into the second equation:\[144 = 56^n\]Solve for \( n \):\[56^n = 144\]To find \( n \), you may need to use logarithms or numerical methods since it may not be straightforward.

Answered by characterailangako | 2024-09-02