what is square root of 145 to 3 sf
The Correct Answer and Explanation is:
The square root of 145 to three significant figures is 12.0.
Explanation:
To find the square root of 145 to three significant figures, you can use a calculator or apply numerical methods such as the Newton-Raphson method. Using a calculator, you get:145≈12.041594578792296\sqrt{145} \approx 12.041594578792296145≈12.041594578792296
When rounding this number to three significant figures, we look at the first three digits that are not zero:
- The first significant digit is 1
- The second is 2
- The third is 0 (from 12.0)
Since the next digit after the third significant figure (which is 4) is less than 5, we do not round up the third figure. Therefore, the value rounded to three significant figures is 12.0.
This means the number has been rounded to show only the first three digits that contribute meaningfully to its value. Significant figures are important in science and engineering because they reflect the precision of a measurement or calculation. Writing 12.0 instead of just 12 implies a degree of precision. It suggests that the measurement is known to the nearest tenth rather than just to the nearest whole number.
It is worth noting that square roots of non-perfect squares are irrational numbers. That means they go on forever without repeating. For example, the square root of 144 is 12 exactly because 144 is a perfect square. However, 145 is not a perfect square, so its square root is irrational. We can only write approximations of it using decimals.
In most practical contexts, such as engineering or physics, using three significant figures provides a good balance between precision and simplicity. Too many digits can complicate calculations unnecessarily, while too few can lead to inaccurate results.
