Find the negative square root of 49.
Multiple choice question. 6 7 -6 -7
The correct answer and explanation is:
The correct answer is -7.
Explanation:
The square root of a number is a value that, when multiplied by itself, gives the original number. The square root can have both a positive and a negative value. For instance, both 7×7=497 \times 7 = 49 and (−7)×(−7)=49(-7) \times (-7) = 49 are true, which means both +7+7 and −7-7 are square roots of 49.
However, when asked for the negative square root, we are specifically looking for the negative value. The negative square root of any positive number is the value that, when squared, gives the original positive number but with a negative sign. Therefore, the negative square root of 49 is -7.
To summarize, the square root of 49 has two possible answers: +7+7 and −7-7. When specifically asked for the negative square root, the answer is −7-7. This principle applies to any positive number. For example, the negative square root of 81 is −9-9, because both 9×9=819 \times 9 = 81 and (−9)×(−9)=81(-9) \times (-9) = 81.
This distinction between positive and negative square roots is essential in solving various mathematical problems, especially when dealing with quadratic equations or when the context specifically requires the negative solution.