Answer :
Sure, let's break this down step-by-step to determine which of the following are the square roots of 441.
1. Understanding square roots: The square root of a number [tex]\( n \)[/tex] is a number [tex]\( x \)[/tex] such that [tex]\( x \times x = n \)[/tex]. For example, if [tex]\( x \)[/tex] is a square root of 441, then [tex]\( x \times x \)[/tex] should equal 441.
2. Finding the square root of 441:
- The positive square root of 441 is 21 because [tex]\( 21 \times 21 = 441 \)[/tex].
- The negative square root of 441 is -21 because [tex]\( -21 \times -21 = 441 \)[/tex].
3. Now let's check each option:
A. [tex]\( 441^{1/2} \)[/tex]:
- [tex]\( 441^{1/2} \)[/tex] represents the positive square root of 441.
- We know that the positive square root is 21.
B. [tex]\( -441^{1/2} \)[/tex]:
- [tex]\( -441^{1/2} \)[/tex] represents the negative square root of 441.
- We know that the negative square root is -21.
C. 882:
- To determine if 882 is a square root of 441, we check if [tex]\( 882 \times 882 = 441 \)[/tex].
- Since [tex]\( 882 \times 882 \neq 441 \)[/tex], 882 is not a square root of 441.
D. -21:
- We know from our earlier work that -21 is a square root of 441 because [tex]\( -21 \times -21 = 441 \)[/tex].
E. 42:
- To determine if 42 is a square root of 441, we check if [tex]\( 42 \times 42 = 441 \)[/tex].
- Since [tex]\( 42 \times 42 \neq 441 \)[/tex], 42 is not a square root of 441.
F. 21:
- We know from our earlier work that 21 is a square root of 441 because [tex]\( 21 \times 21 = 441 \)[/tex].
Therefore, the correct answers are A ([tex]\( 441^{1 / 2} \)[/tex]), B ([tex]\( -441^{1 / 2} \)[/tex]), D (-21), and F (21).
1. Understanding square roots: The square root of a number [tex]\( n \)[/tex] is a number [tex]\( x \)[/tex] such that [tex]\( x \times x = n \)[/tex]. For example, if [tex]\( x \)[/tex] is a square root of 441, then [tex]\( x \times x \)[/tex] should equal 441.
2. Finding the square root of 441:
- The positive square root of 441 is 21 because [tex]\( 21 \times 21 = 441 \)[/tex].
- The negative square root of 441 is -21 because [tex]\( -21 \times -21 = 441 \)[/tex].
3. Now let's check each option:
A. [tex]\( 441^{1/2} \)[/tex]:
- [tex]\( 441^{1/2} \)[/tex] represents the positive square root of 441.
- We know that the positive square root is 21.
B. [tex]\( -441^{1/2} \)[/tex]:
- [tex]\( -441^{1/2} \)[/tex] represents the negative square root of 441.
- We know that the negative square root is -21.
C. 882:
- To determine if 882 is a square root of 441, we check if [tex]\( 882 \times 882 = 441 \)[/tex].
- Since [tex]\( 882 \times 882 \neq 441 \)[/tex], 882 is not a square root of 441.
D. -21:
- We know from our earlier work that -21 is a square root of 441 because [tex]\( -21 \times -21 = 441 \)[/tex].
E. 42:
- To determine if 42 is a square root of 441, we check if [tex]\( 42 \times 42 = 441 \)[/tex].
- Since [tex]\( 42 \times 42 \neq 441 \)[/tex], 42 is not a square root of 441.
F. 21:
- We know from our earlier work that 21 is a square root of 441 because [tex]\( 21 \times 21 = 441 \)[/tex].
Therefore, the correct answers are A ([tex]\( 441^{1 / 2} \)[/tex]), B ([tex]\( -441^{1 / 2} \)[/tex]), D (-21), and F (21).
