Question

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

Answer 1

4 Answers: B, C, D, and F

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Step-by-step explanation:

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

This shows that 19 is a square root of 361. We can say
`√(361) = √(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) = √(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.

Answer 2

strangely worded question....

`361^(1/2) = √(361)`

Step-by-step explanation: