Between which two consecutive whole number does the square root of 38 lie
The Correct Answer and Explanation is :
The correct answer is: 6 and 7
The square root of 38 lies between two consecutive whole numbers: 6 and 7.
Here’s why:
Step 1: Identify perfect squares near 38.
We need to find two perfect squares, one smaller and one larger than 38. Let’s check the squares of numbers close to 38:
- ( 6^2 = 36 )
- ( 7^2 = 49 )
So, 38 is between 36 and 49.
Step 2: Understand that square roots are increasing between perfect squares.
The square root of a number increases gradually as you move from one perfect square to the next. Since 38 is between 36 and 49, its square root must be between the square roots of those numbers:
- ( \sqrt{36} = 6 )
- ( \sqrt{49} = 7 )
Thus, the square root of 38 must be between 6 and 7.
Step 3: Estimate more precisely.
Since 38 is closer to 36 than 49, we can estimate that the square root of 38 is a little greater than 6 but less than 7. You could refine the approximation further using methods like the average of 6 and 7 or a calculator, but for this task, it’s enough to say:
- ( 6 < \sqrt{38} < 7 )
Conclusion:
The square root of 38 lies between the whole numbers 6 and 7 because the squares of these numbers (36 and 49) bracket 38. Without needing to calculate the exact value, you know it’s a bit more than 6 but less than 7.