Question

Which of the following square root of the following number below? Check all that apply. 361

Answer 1

Answer:

strangely worded question....

$361^{1/2} = \sqrt{361}$

Step-by-step explanation:

Answer 2

4 Answers:  B, C, D, and F

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Explanation:

Notice how (19)^2 = 19*19 = 361

This shows that 19 is a square root of 361. We can say $\sqrt{361} = \sqrt{19^2} = 19$

Similarly, (-19)^2 = (-19)*(-19) = 361. The two negatives cancel each other out. So that's why there are two solutions to $x^2 = 361$ which are x = 19 and x = -19.

So far that accounts for answer choices B and D.

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The other two answers are $-361^{1/2}$ and $361^{1/2}$ (choices C and F) because anything to the 1/2 power represents a square root.

$x^{1/2} = \sqrt{x}$

anything to the 1/3 power is a cube root

$x^{1/3} = \sqrt[3]{x}$

anything to the 1/4 power is a fourth root

$x^{1/4} = \sqrt[4]{x}$

and so on.

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Side note: For choice C, the exponent is done first before we apply the negative. So technically we could say $-1*(361)^{1/2}$ for choice C to mean the same exact thing. If your teacher said $(-361)^{1/2}$ then this would not be an answer because this results in a non-real number.