Question:** Suppose that \( v \) is a positive multiple of 5. If \( v^2 \) is less than 600, what is the greatest possible value of \( v \)?

["Title: What is the Greatest Positive Multiple of 5 Whose Square Is Less Than 600?", "Meta Description:\nFind the greatest positive multiple of 5 such that its square is less than 600. Learn how to solve this math problem step by step with clear reasoning and best practices.", "---", "### Suppose ( v ) is a positive multiple of 5. If ( v^2 < 600 ), what is the greatest possible value of ( v )?", "When exploring mathematical constraints involving multiples and inequalities, identifying the largest valid solution is a common challenge. In this case, we’re given that ( v ) is a positive multiple of 5, and that ( v^2 < 600 ). Our goal is to find the greatest such ( v ) satisfying both conditions.", "---", "### Step 1: Understand the Constraint", "Since ( v ) is a positive multiple of 5, it takes values like:", "[ v = 5, 10, 15, 20, 25, 30, 35, \dots ]", "But ( v^2 ) must be less than 600:", "[\nv^2 < 600\n]", "To find the maximum possible ( v ), we need to determine the largest multiple of 5 whose square remains under 600.", "---", "### Step 2: Estimate the Upper Bound", "We solve the inequality:", "[\nv < \sqrt{600}\n]", "Calculating the square root:", "[\n\sqrt{600} \approx 24.49\n]", "This means ( v ) must be less than 24.49. Since ( v ) must be a multiple of 5, we look for the largest multiple of 5 below 24.49.", "---", "### Step 3: List Valid Multiples Below the Limit", "The multiples of 5 below 24.49 are:", "[\n5, 10, 15, 20\n]", "The next multiple, 25, is too large because:", "[\n25^2 = 625 \quad \ ext{(which exceeds 600)}\n]", "---", "### Step 4: Verify the Greatest Valid Value", "Check the square of the largest candidate:", "- ( 20^2 = 400 < 600 ) ✅\n- ( 25^2 = 625 <br/>\not< 600 ) ❌", "Thus, 20 is the greatest positive multiple of 5 for which ( v^2 < 600 ).", "---", "### Final Answer", "The greatest possible value of ( v ) is:", "[\n\boxed{20}\n]", "---", "### Why This Method Works", "By combining the condition of being a multiple of 5 with the inequality constraint, we efficiently narrow the candidate values. Instead of checking every number, we:", "- Use square root estimation to bound the solution\n- Identify multiples directly based on that bound\n- Test and confirm the largest valid candidate", "This structured approach applies smoothly to similar math problems involving multiples and inequalities.", "---", "Keywords: positive multiple of 5, largest ( v ) where ( v^2 < 600 ), math problem solving, square root estimate, inequality with multiples", "Visit again for more tips on solving number and inequality-based math questions."]