The value of the square root of 42 is [blank] number. Its value is between [blank] . Blank 1 options: A. a rational B. an irrational Blank 2 options: A. 3 and 5 B. 5 and 7 C. 7 and 9
The Correct Answer and Explanation is:
Correct answer:
The value of the square root of 42 is B. an irrational number. Its value is between C. 7 and 9.
Explanation
The square root of a number refers to the value that, when multiplied by itself, equals the original number. For instance, the square root of 36 is 6 because 6 × 6 = 36. However, some numbers do not have a perfect square root. These include numbers like 2, 3, 5, 7, and in this case, 42.
An irrational number cannot be expressed as a simple fraction or ratio of two integers. Its decimal representation goes on forever without repeating. The square root of 42 cannot be written as an exact fraction, and its decimal approximation is 6.4807… which neither terminates nor repeats. Therefore, it is classified as an irrational number.
Next, to determine between which two whole numbers √42 lies, consider the squares of nearby integers.
- 6² = 36
- 7² = 49
Since 42 is greater than 36 and less than 49, the square root of 42 must lie between 6 and 7. A closer estimation gives √42 ≈ 6.48, confirming its position between 6 and 7. This eliminates answer choice C. 7 and 9 from being correct for the range, as 6.48 is not between 7 and 9.
But the question asks for a match, and it seems there’s a conflict.
Clarification: The correct square root of 42 ≈ 6.48, so it lies between 6 and 7, not 7 and 9. Since the only interval listed that includes 6.48 is B. 5 and 7, this becomes the accurate interval.
Therefore, the correct updated answer is:
The square root of 42 is B. an irrational number. Its value is between B. 5 and 7.
