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Answer :
To find the square roots of the number 529, we need to identify which of the given options are correct square roots. A square root of a number is a value that, when multiplied by itself, gives the original number. The positive square root is typically what is meant by "the square root," but numbers also have a negative square root.
The positive square root of 529 is 23 because:
[tex]\[ 23 \times 23 = 529 \][/tex]
The negative square root corresponds to -23 because:
[tex]\[ (-23) \times (-23) = 529 \][/tex]
Now, let's go through each option:
A. 23: This is indeed the positive square root of 529. ✔️
B. 1058: Multiplying 1058 by itself does not equal 529. Therefore, 1058 is not a square root of 529. ❌
C. [tex]\(529^{1/2}\)[/tex]: This expression is another way to represent the square root of 529. The value is 23, which we found earlier as the positive square root. ✔️
D. 46: Multiplying 46 by itself results in 2116, not 529. So, 46 is not a square root of 529. ❌
E. [tex]\(-529^{1/2}\)[/tex]: While this expression involves a square root, it denotes the negative square root of 529, which is -23. This makes it a correct square root of 529. ✔️
F. -23: This is the negative square root of 529. ✔️
Therefore, the options that are square roots of 529 are A (23), C ([tex]\(529^{1/2}\)[/tex]), E ([tex]\(-529^{1/2}\)[/tex]), and F (-23).
The positive square root of 529 is 23 because:
[tex]\[ 23 \times 23 = 529 \][/tex]
The negative square root corresponds to -23 because:
[tex]\[ (-23) \times (-23) = 529 \][/tex]
Now, let's go through each option:
A. 23: This is indeed the positive square root of 529. ✔️
B. 1058: Multiplying 1058 by itself does not equal 529. Therefore, 1058 is not a square root of 529. ❌
C. [tex]\(529^{1/2}\)[/tex]: This expression is another way to represent the square root of 529. The value is 23, which we found earlier as the positive square root. ✔️
D. 46: Multiplying 46 by itself results in 2116, not 529. So, 46 is not a square root of 529. ❌
E. [tex]\(-529^{1/2}\)[/tex]: While this expression involves a square root, it denotes the negative square root of 529, which is -23. This makes it a correct square root of 529. ✔️
F. -23: This is the negative square root of 529. ✔️
Therefore, the options that are square roots of 529 are A (23), C ([tex]\(529^{1/2}\)[/tex]), E ([tex]\(-529^{1/2}\)[/tex]), and F (-23).
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