Answer :
To find the square roots of 441, we need to determine which options are valid when they are squared back to give the number 441.
Let's look at the options one by one:
A. -21
When -21 is squared, [tex]\((-21) \times (-21) = 441\)[/tex]. So, -21 is a square root of 441.
B. [tex]\(441^{1/2}\)[/tex]
This expression represents the positive square root of 441, which is 21. So, [tex]\(441^{1/2} = 21\)[/tex], meaning it is a valid square root of 441.
C. 882
When 882 is squared, it does not give 441. So, 882 is not a square root of 441.
D. 21
When 21 is squared, [tex]\(21 \times 21 = 441\)[/tex]. So, 21 is a square root of 441.
E. [tex]\(-441^{1/2}\)[/tex]
This expression represents the negative square root of 441, which is -21. Therefore, [tex]\(-441^{1/2} = -21\)[/tex], and it is a valid square root of 441.
F. 42
When 42 is squared, it does not give 441. So, 42 is not a square root of 441.
Therefore, the valid square roots of 441 are A. -21, B. [tex]\(441^{1/2}\)[/tex], D. 21, and E. [tex]\(-441^{1/2}\)[/tex].
Let's look at the options one by one:
A. -21
When -21 is squared, [tex]\((-21) \times (-21) = 441\)[/tex]. So, -21 is a square root of 441.
B. [tex]\(441^{1/2}\)[/tex]
This expression represents the positive square root of 441, which is 21. So, [tex]\(441^{1/2} = 21\)[/tex], meaning it is a valid square root of 441.
C. 882
When 882 is squared, it does not give 441. So, 882 is not a square root of 441.
D. 21
When 21 is squared, [tex]\(21 \times 21 = 441\)[/tex]. So, 21 is a square root of 441.
E. [tex]\(-441^{1/2}\)[/tex]
This expression represents the negative square root of 441, which is -21. Therefore, [tex]\(-441^{1/2} = -21\)[/tex], and it is a valid square root of 441.
F. 42
When 42 is squared, it does not give 441. So, 42 is not a square root of 441.
Therefore, the valid square roots of 441 are A. -21, B. [tex]\(441^{1/2}\)[/tex], D. 21, and E. [tex]\(-441^{1/2}\)[/tex].
