Square root of 43 on a number line?
The correct answer and explanation is:
The square root of 43 is approximately 6.557. To understand how this value fits on a number line, it’s essential to first know that square roots represent the value that, when multiplied by itself, equals the given number. So, the square root of 43 is the number that, when squared, gives you 43.
On a number line, this value falls between the whole numbers 6 and 7. This is because:
- 6 squared (6 × 6) equals 36.
- 7 squared (7 × 7) equals 49.
Since 43 is between 36 and 49, the square root of 43 must be between 6 and 7. More specifically, since 43 is closer to 49 than to 36, the square root will be closer to 7 than to 6. The approximation of 6.557 places it slightly above the midpoint between 6 and 7, but still closer to 6 than to 7.
To visually represent this on a number line:
- Mark points for 6 and 7.
- Divide the segment between 6 and 7 into smaller increments.
- Estimate the position of 6.557, which is a bit above the middle of the 6-7 range, but not as close to 7 as it is to 6.
In summary, the square root of 43 (approximately 6.557) can be located between 6 and 7 on a number line, slightly closer to 7 than to 6. This value is an irrational number, meaning it has infinite non-repeating decimals, which is why the representation on the number line is an approximation.