What is the square root of 8648?
Understand the Problem
The question is about solving a mathematical expression, specifically the square root of 8648. The user is likely looking for a step-by-step solution to find the square root.
Answer
The approximate value of the square root of 8648 is $ \approx 92.9 $.
Answer for screen readers
The approximate value of the square root of 8648 is $ \approx 92.9 $.
Steps to Solve
-
Estimate the square root To find the square root of 8648, start by estimating between two perfect squares. The square root of 8648 falls between the square root of 8100 (which is 90) and the square root of 9409 (which is 97).
-
Refine the estimate Let's refine our estimate. Start with 92: $$ 92^2 = 8464 $$
Next, try 93: $$ 93^2 = 8649 $$
Since $8648$ is slightly less than $8649$, the square root is slightly less than 93.
- Use approximation for precision You can refine further by trying numbers closer to 92 and 93. For example, try 92.9: $$ 92.9^2 = 8648.41 $$
And 92.8: $$ 92.8^2 = 8616.64 $$
Since $8648$ is between $8616.64$ and $8648.41$, the square root of $8648$ is approximately $92.9$.
The approximate value of the square root of 8648 is $ \approx 92.9 $.
More Information
Finding the square root of larger numbers often requires estimation and refinement. The method used here approximates values by testing nearby integers and decimals.
Tips
- Skipping the estimation step: Always estimate the square root before calculating.
- Not checking both sides of the target value: Ensure you test values above and below the square root to narrow down accurately.
AI-generated content may contain errors. Please verify critical information
