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Which of the following are square roots of the number below? Check all that apply.

529

A. -23
B. [tex]529^{1 / 2}[/tex]
C. 1058
D. 46
E. 23
F. [tex]-529^{1 / 2}[/tex]

Answer :

Let's find the square roots of the number 529 and check which options apply:

1. Determine the positive square root:
- The number 529 is a perfect square, and its positive square root is 23. This means 23 × 23 = 529.

2. Determine the negative square root:
- The negative square root of a number is simply the negative of its positive square root. So, for 529, the negative square root is -23.

Now, let's check each given option:

- A. -23: This is correct because -23 is a square root of 529.
- B. [tex]\(529^{1 / 2}\)[/tex]: This notation means to take the square root of 529, which equals 23. So, this is correct.
- C. 1058: This is incorrect since 1058 squared does not equal 529.
- D. 46: This is incorrect because 46 squared does not equal 529.
- E. 23: This is correct because 23 is the positive square root of 529.
- F. [tex]\(-529^{1 / 2}\)[/tex]: This means to take the negative square root of 529, which equals -23. So, this is correct.

Therefore, the square roots of 529 are -23, [tex]\(529^{1 / 2}\)[/tex], 23, and [tex]\(-529^{1 / 2}\)[/tex]. The correct options are A, B, E, and F.

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