Directions (20-23): What approximate value will come in place of the q...
Understanding the Expression
To solve the expression √5183.98 ÷ √36, we can simplify it using properties of square roots.
Properties of Square Roots
- The property states that √a ÷ √b = √(a/b).
- Therefore, we can rewrite the expression as: √(5183.98 / 36).
Estimating the Values
1. Estimate √36:
- We know that √36 = 6.
2. Estimate 5183.98 / 36:
- To simplify, we can round 5183.98 to approximately 5184.
- Now, we perform the division: 5184 ÷ 36.
- A rough estimate can be calculated as follows:
- 36 is close to 40, so we can first find 5184 ÷ 40.
- 5184 ÷ 40 is approximately 129.6.
3. Finding the Square Root:
- Now we need to estimate √129.6.
- We know that √121 = 11 and √144 = 12.
- Since 129.6 is closer to 121, we can approximate that √129.6 is around 11.4.
Final Calculation
Putting it all together, we have:
- √5183.98 ÷ √36 ≈ √(129.6) ≈ 11.4.
Since we are looking for an approximate value, the closest option available is:
Conclusion
- The answer is approximately 12, which corresponds to option 'c'.