Answer :
To solve the equation [tex]\(x^2 = 49\)[/tex], we need to find which numbers, when squared, equal 49. Let's go through the given options one by one:
A. 2401: When you square 2401 ([tex]\(2401 \times 2401\)[/tex]), the result is much larger than 49. So, 2401 is not a solution.
B. 24.5: Squaring 24.5 ([tex]\(24.5 \times 24.5\)[/tex]) gives a number greater than 49. Thus, 24.5 is not a solution.
C. 49: Squaring 49 ([tex]\(49 \times 49\)[/tex]) results in 2401, which is not equal to 49. Hence, 49 is not a solution to the equation.
D. 7: When you square 7 ([tex]\(7 \times 7\)[/tex]), you exactly get 49. So, 7 is a solution.
E. -7: Squaring -7 ([tex]\((-7) \times (-7)\)[/tex]) also gives 49. Therefore, -7 is a solution as well.
F. None of these: Since we've found numbers that are solutions (7 and -7), this option is not correct.
So, the solutions to the equation [tex]\(x^2 = 49\)[/tex] are 7 and -7.
A. 2401: When you square 2401 ([tex]\(2401 \times 2401\)[/tex]), the result is much larger than 49. So, 2401 is not a solution.
B. 24.5: Squaring 24.5 ([tex]\(24.5 \times 24.5\)[/tex]) gives a number greater than 49. Thus, 24.5 is not a solution.
C. 49: Squaring 49 ([tex]\(49 \times 49\)[/tex]) results in 2401, which is not equal to 49. Hence, 49 is not a solution to the equation.
D. 7: When you square 7 ([tex]\(7 \times 7\)[/tex]), you exactly get 49. So, 7 is a solution.
E. -7: Squaring -7 ([tex]\((-7) \times (-7)\)[/tex]) also gives 49. Therefore, -7 is a solution as well.
F. None of these: Since we've found numbers that are solutions (7 and -7), this option is not correct.
So, the solutions to the equation [tex]\(x^2 = 49\)[/tex] are 7 and -7.
