To find the square roots of 49, we need to determine the numbers that, when multiplied by themselves, equal 49.
Let's consider the positive square root first:
1. We start by identifying a number whose square is 49.
2. We check the possibilities: [tex]\(1^2 = 1\)[/tex], [tex]\(2^2 = 4\)[/tex], [tex]\(3^2 = 9\)[/tex], [tex]\(4^2 = 16\)[/tex], [tex]\(5^2 = 25\)[/tex], [tex]\(6^2 = 36\)[/tex], [tex]\(7^2 = 49\)[/tex].
We see that [tex]\(7^2 = 49\)[/tex]. Therefore, one square root of 49 is 7.
Next, let's consider that there is also a negative square root:
1. We recognize that squaring a negative number also results in a positive number because [tex]\((-x)^2 = x^2\)[/tex].
2. Since [tex]\(7^2 = 49\)[/tex], [tex]\((-7)^2\)[/tex] must also be 49.
Thus, the negative square root of 49 is -7.
So the square roots of 49 are:
7 and -7.
From the given choices:
- 5 and -5: This is incorrect because [tex]\(5^2 = 25\)[/tex] and [tex]\((-5)^2 = 25\)[/tex].
- 6 and -6: This is incorrect because [tex]\(6^2 = 36\)[/tex] and [tex]\((-6)^2 = 36\)[/tex].
- 7 and -7: This is correct because [tex]\(7^2 = 49\)[/tex] and [tex]\((-7)^2 = 49\)[/tex].
- 8 and -8: This is incorrect because [tex]\(8^2 = 64\)[/tex] and [tex]\((-8)^2 = 64\)[/tex].
Therefore, the correct answer is:
7 and -7.
