Update solver.py

solver.py

@@ -114,25 +114,47 @@ def process_expression(expr_str):
             return f"d/dx({format_expression(expr)}) = {format_expression(result)}"
         
         
-        elif 'sqrt' in processed_expr:  # Handle square roots
+        elif 'sqrt' in processed_expr.lower():  
             try:
                 transformations = standard_transformations + (implicit_multiplication_application,)
-                expr = sp.parse_expr(processed_expr, transformations=transformations)
-
-                sqrt_result = sqrt(expr)  # Compute square root
-                positive_root = sqrt_result
-                negative_root = -sqrt_result
-
+        
+        # Remove "sqrt" and parse the expression inside
+                expr = sp.parse_expr(processed_expr.replace("sqrt", ""), transformations=transformations)  
+        
+                sqrt_result = sp.sqrt(expr)  
+        
+        # If it's sqrt(x^2), simplify it to |x|
+                simplified_result = sp.simplify(sqrt_result)
+        
                 steps = []
-                steps.append(f"**Step 1:** Original expression: \n{latex(expr)}")
-                steps.append(f"**Step 2:** Taking square root: \n{latex(sqrt_result)}")
-                steps.append(f"**Step 3:** Considering both positive and negative roots: \n±{latex(sqrt_result)}")
-
-                solution = "\n".join(steps)
+                steps.append(f"**Step 1:** Original expression: \n{to_latex(expr)}")
+        
+        # Case 1: Perfect Squares → Show exact value (e.g., sqrt(9) = ±3)
+                if sqrt_result.is_Integer:
+                    steps.append(f"**Step 2:** √{to_latex(expr)} is a perfect square")
+                    steps.append(f"**Step 3:** Solution: \n±{to_latex(sqrt_result)}")
+                    solution = "\n".join(steps)
+
+        # Case 2: Non-Perfect Squares → Show decimal value (e.g., sqrt(2) ≈ 1.41)
+                elif sqrt_result.is_real and not sqrt_result.is_rational:
+                    decimal_value = float(sqrt_result.evalf())
+                    steps.append(f"**Step 2:** √{to_latex(expr)} is not a perfect square")
+                    steps.append(f"**Step 3:** Approximate value: \n{decimal_value}")
+                    solution = "\n".join(steps)
+
+        # Case 3: Expressions like √x² → |x|
+                elif simplified_result != sqrt_result:
+                    steps.append(f"**Step 2:** Simplification using identity: \n{to_latex(simplified_result)}")
+                    solution = "\n".join(steps)
+
+        # Case 4: General Expression → Return as-is
+                else:
+                    steps.append(f"**Step 2:** Taking square root: \n{to_latex(sqrt_result)}")
+                    steps.append(f"**Step 3:** Considering both positive and negative roots: \n±{to_latex(sqrt_result)}")
+                    solution = "\n".join(steps)
 
             except Exception as e:
-             solution = f"Error: {str(e)}"
-
+                solution = f"Error: {str(e)}"
         elif 'factorial' in processed_expr:  # Factorial case
             expr = parse_expr(processed_expr, transformations=(standard_transformations + (implicit_multiplication_application,)))
             result = expr.doit()  # Compute the factorial correctly