Answer :
To find the square roots of the number 441, let's break down the options provided:
1. Understand what a square root is: A square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we're looking for numbers that show [tex]\((\text{some number}) \times (\text{same number}) = 441\)[/tex].
2. Calculate the square root of 441:
- 441 is a perfect square, which means there is a whole number that is its square root.
- The positive square root of 441 is 21 because [tex]\(21 \times 21 = 441\)[/tex].
3. Check for negative square root:
- In mathematics, there are typically two square roots for positive numbers: one positive and one negative. So, [tex]\(-21\)[/tex] is also a square root because [tex]\(-21 \times -21 = 441\)[/tex].
Now, let's review the options:
- A. 882: This is not correct because if you multiply 882 by itself, you would get a number much larger than 441.
- B. [tex]\(441^{1 / 2}\)[/tex]: This notation represents the square root of 441, which is 21, so this option is correct.
- C. -21: As discussed, because [tex]\(-21 \times -21 = 441\)[/tex], this option is correct.
- D. [tex]\(-441^{1 / 2}\)[/tex]: This notation represents the negative of the square root of 441, which is -21, so this option is correct.
- E. 21: This is the positive square root of 441, so this option is correct.
- F. 42: This is not correct because [tex]\(42 \times 42 = 1764\)[/tex], which is much larger than 441.
Therefore, the correct answers for the square roots of 441 are options B, C, D, and E.
1. Understand what a square root is: A square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we're looking for numbers that show [tex]\((\text{some number}) \times (\text{same number}) = 441\)[/tex].
2. Calculate the square root of 441:
- 441 is a perfect square, which means there is a whole number that is its square root.
- The positive square root of 441 is 21 because [tex]\(21 \times 21 = 441\)[/tex].
3. Check for negative square root:
- In mathematics, there are typically two square roots for positive numbers: one positive and one negative. So, [tex]\(-21\)[/tex] is also a square root because [tex]\(-21 \times -21 = 441\)[/tex].
Now, let's review the options:
- A. 882: This is not correct because if you multiply 882 by itself, you would get a number much larger than 441.
- B. [tex]\(441^{1 / 2}\)[/tex]: This notation represents the square root of 441, which is 21, so this option is correct.
- C. -21: As discussed, because [tex]\(-21 \times -21 = 441\)[/tex], this option is correct.
- D. [tex]\(-441^{1 / 2}\)[/tex]: This notation represents the negative of the square root of 441, which is -21, so this option is correct.
- E. 21: This is the positive square root of 441, so this option is correct.
- F. 42: This is not correct because [tex]\(42 \times 42 = 1764\)[/tex], which is much larger than 441.
Therefore, the correct answers for the square roots of 441 are options B, C, D, and E.
