The value of square root 180 is lies between dash and dash integers
The Correct Answer and Explanation is:
To find the square root of 180 and determine between which two integers it lies, let’s go step by step.
Step 1: Estimate the square root
We know that:
- The square of 13 is 169: 132=16913^2 = 169132=169
- The square of 14 is 196: 142=19614^2 = 196142=196
The number 180 is between 169 and 196, so the square root of 180 must be between 13 and 14.
Step 2: Refine the estimate
Now, let’s get a more accurate value for 180\sqrt{180}180. Using a calculator or estimation method, we find that: 180≈13.416\sqrt{180} \approx 13.416180≈13.416
This value is clearly closer to 13 than to 14, but it is still between these two integers.
Step 3: Understanding the square root
The square root of any number xxx is the value yyy such that y2=xy^2 = xy2=x. In this case, the square root of 180 is the value that, when squared, gives 180. Since 180 is closer to 169 (13 squared) than it is to 196 (14 squared), we know that the square root lies between 13 and 14.
Conclusion
The square root of 180 lies between the integers 13 and 14. Specifically, it is a little more than 13, at approximately 13.416, which means it is greater than 13 but less than 14.
By estimating, squaring numbers, and refining our guess, we can determine the square root’s approximate value and conclude that it is between the integers 13 and 1
