The possible one digit in the square root of 1369 is
The Correct Answer and Explanation is:
Correct Answer: The possible one-digit in the square root of 1369 is 7.
To determine the one-digit value in the square root of 1369, begin by calculating the square root directly. The square root of a number is a value which, when multiplied by itself, gives the original number. So, the square root of 1369 can be found by identifying a number that satisfies this condition.
Using multiplication:37×37=136937 \times 37 = 136937×37=1369
This confirms that 37 is the square root of 1369. Since the question asks for the one-digit in the square root, attention is drawn to the units digit of 37, which is 7.
This digit holds importance in various mathematical checks. When squaring numbers, the units digit of the result often corresponds to a predictable pattern from the units digit of the original number. For instance, a number ending in 7 squared (like 7 × 7 = 49) results in a units digit of 9. In this case, 1369 ends in a 9, and that aligns with the square of a number ending in 3 or 7, both of which can produce a square ending in 9. That narrows the square root possibilities to numbers ending in either 3 or 7.
To determine which of these is correct, squaring both candidates helps:
- 33 × 33 = 1089
- 37 × 37 = 1369
Only 37 satisfies the condition. Thus, the correct square root is 37, and the one-digit in question is 7.
The logic here highlights the usefulness of units-digit patterns in squaring and square roots. Understanding these patterns can guide number recognition and estimation in mental math without needing full multiplication every time.
