Answer :
To find which of the given numbers are solutions to the equation [tex]\( x^2 = -7 \)[/tex], we need to check which of these numbers, when squared, equals [tex]\(-7\)[/tex].
Here's the step-by-step process:
1. Squaring [tex]\(-\sqrt{7}\)[/tex]:
[tex]\[
(-\sqrt{7})^2 = (\sqrt{7})^2 = 7 \quad (\text{which is not } -7)
\][/tex]
2. Squaring 49:
[tex]\[
49^2 = 49 \times 49 = 2401 \quad (\text{which is not } -7)
\][/tex]
3. Squaring -3.5:
[tex]\[
(-3.5)^2 = 3.5^2 = 12.25 \quad (\text{which is not } -7)
\][/tex]
4. Squaring [tex]\(\sqrt{7}\)[/tex]:
[tex]\[
(\sqrt{7})^2 = 7 \quad (\text{which is not } -7)
\][/tex]
5. Squaring -7:
[tex]\[
(-7)^2 = 49 \quad (\text{which is not } -7)
\][/tex]
After evaluating each option, we see that:
- None of the numbers [tex]\(-\sqrt{7}, 49, -3.5, \sqrt{7},\)[/tex] and [tex]\(-7\)[/tex] satisfy the equation [tex]\( x^2 = -7 \)[/tex].
Therefore, the answer is:
F. None of these
Here's the step-by-step process:
1. Squaring [tex]\(-\sqrt{7}\)[/tex]:
[tex]\[
(-\sqrt{7})^2 = (\sqrt{7})^2 = 7 \quad (\text{which is not } -7)
\][/tex]
2. Squaring 49:
[tex]\[
49^2 = 49 \times 49 = 2401 \quad (\text{which is not } -7)
\][/tex]
3. Squaring -3.5:
[tex]\[
(-3.5)^2 = 3.5^2 = 12.25 \quad (\text{which is not } -7)
\][/tex]
4. Squaring [tex]\(\sqrt{7}\)[/tex]:
[tex]\[
(\sqrt{7})^2 = 7 \quad (\text{which is not } -7)
\][/tex]
5. Squaring -7:
[tex]\[
(-7)^2 = 49 \quad (\text{which is not } -7)
\][/tex]
After evaluating each option, we see that:
- None of the numbers [tex]\(-\sqrt{7}, 49, -3.5, \sqrt{7},\)[/tex] and [tex]\(-7\)[/tex] satisfy the equation [tex]\( x^2 = -7 \)[/tex].
Therefore, the answer is:
F. None of these
